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Journal articles on the topic 'Monotonicity formulae'

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Published: 10 March 2023

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1

Engelfriet, J. "Monotonicity and Persistence in Preferential Logics." Journal of Artificial Intelligence Research 8 (January 1, 1998): 1–21. http://dx.doi.org/10.1613/jair.461.

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An important characteristic of many logics for Artificial Intelligence is their nonmonotonicity. This means that adding a formula to the premises can invalidate some of the consequences. There may, however, exist formulae that can always be safely added to the premises without destroying any of the consequences: we say they respect monotonicity. Also, there may be formulae that, when they are a consequence, can not be invalidated when adding any formula to the premises: we call them conservative. We study these two classes of formulae for preferential logics, and show that they are closely linked to the formulae whose truth-value is preserved along the (preferential) ordering. We will consider some preferential logics for illustration, and prove syntactic characterization results for them. The results in this paper may improve the efficiency of theorem provers for preferential logics.

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2

Djaa, Nour Elhouda, Ahmed Mohamed Cherif, and Kaddour Zegga. "Monotonicity formulae and F-stress energy." Bulletin of the Transilvania University of Brasov Series III Mathematics and Computer Science 1(63), no. 1 (October 7, 2021): 81–96. http://dx.doi.org/10.31926/but.mif.2021.1.63.1.7.

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The goal of this work is the application of the f-stress energy of differ-ential forms to study the generalized monotonicity formulae and generalizedvanishing theorems. We obtain some generalized monotonicity formulas forp-formsω∈Ap(ξ), which satisfy the generalizedf-conservation laws, withf∈C∞(M×R) satisfying some conditions

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3

Evans, Lawrence C. "Monotonicity formulae for variational problems." Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences 371, no. 2005 (December 28, 2013): 20120339. http://dx.doi.org/10.1098/rsta.2012.0339.

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4

Li, Jintang. "Monotonicity formulae and vanishing theorems." Pacific Journal of Mathematics 281, no. 1 (February 9, 2016): 125–36. http://dx.doi.org/10.2140/pjm.2016.281.125.

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5

Fazly, Mostafa, and Juncheng Wei. "On stable solutions of the fractional Hénon–Lane–Emden equation." Communications in Contemporary Mathematics 18, no. 05 (July 18, 2016): 1650005. http://dx.doi.org/10.1142/s021919971650005x.

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We derive monotonicity formulae for solutions of the fractional Hénon–Lane–Emden equation [Formula: see text] when [Formula: see text], [Formula: see text] and [Formula: see text]. Then, we apply these formulae to classify stable solutions of the above equation.

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6

Fazly, Mostafa, and Henrik Shahgholian. "Monotonicity formulas for coupled elliptic gradient systems with applications." Advances in Nonlinear Analysis 9, no. 1 (June 6, 2019): 479–95. http://dx.doi.org/10.1515/anona-2020-0010.

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Abstract Consider the following coupled elliptic system of equations $$\begin{array}{} \displaystyle (-{\it\Delta})^s u_i = (u^2_1+\cdots+u^2_m)^{\frac{p-1}{2}} u_i \quad \text{in} ~~ \mathbb{R}^n , \end{array}$$ where 0 < s ≤ 2, p > 1, m ≥ 1, u = $\begin{array}{} \displaystyle (u_i)_{i=1}^m \end{array}$ and ui : ℝn → ℝ. The qualitative behavior of solutions of the above system has been studied from various perspectives in the literature including the free boundary problems and the classification of solutions. For the case of local scalar equation, that is when m = 1 and s = 1, Gidas and Spruck in [26] and later Caffarelli, Gidas and Spruck in [6] provided the classification of solutions for Sobolev sub-critical and critical exponents. More recently, for the case of local system of equations that is when m ≥ 1 and s = 1 a similar classification result is given by Druet, Hebey and Vétois in [17] and references therein. In this paper, we derive monotonicity formulae for entire solutions of the above local, when s = 1, 2, and nonlocal, when 0 < s < 1 and 1 < s < 2, system. These monotonicity formulae are of great interests due to the fact that a counterpart of the celebrated monotonicity formula of Alt-Caffarelli-Friedman [1] seems to be challenging to derive for system of equations. Then, we apply these formulae to give a classification of finite Morse index solutions. In the end, we provide an open problem in regards to monotonicity formulae for Lane-Emden systems.

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7

Wang, Jiaxiang, and Bin Zhou. "Monotonicity formulae for the complex Hessian equations." Methods and Applications of Analysis 28, no. 1 (2021): 77–84. http://dx.doi.org/10.4310/maa.2021.v28.n1.a6.

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8

Nikolov, Geno. "On the monotonicity of sequences of quadrature formulae." Numerische Mathematik 62, no. 1 (December 1992): 557–65. http://dx.doi.org/10.1007/bf01396243.

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9

Fried, Eliot, and Luca Lussardi. "Monotonicity formulae for smooth extremizers of integral functionals." Rendiconti Lincei - Matematica e Applicazioni 30, no. 2 (June 21, 2019): 365–77. http://dx.doi.org/10.4171/rlm/851.

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10

Dong, Y., and H. Lin. "MONOTONICITY FORMULAE, VANISHING THEOREMS AND SOME GEOMETRIC APPLICATIONS." Quarterly Journal of Mathematics 65, no. 2 (March 28, 2013): 365–97. http://dx.doi.org/10.1093/qmath/hat009.

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11

Dong, Yuxin. "Monotonicity formulae and holomorphicity of harmonic maps between Kähler manifolds." Proceedings of the London Mathematical Society 107, no. 6 (May 12, 2013): 1221–60. http://dx.doi.org/10.1112/plms/pdt014.

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12

Zhu, Jonathan J. "Moving-centre monotonicity formulae for minimal submanifolds and related equations." Journal of Functional Analysis 274, no. 5 (March 2018): 1530–52. http://dx.doi.org/10.1016/j.jfa.2017.07.008.

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13

Lin, Hezi, Guilin Yang, Yibin Ren, and Tian Chong. "Monotonicity formulae and Liouville theorems of harmonic maps with potential." Journal of Geometry and Physics 62, no. 9 (September 2012): 1939–48. http://dx.doi.org/10.1016/j.geomphys.2012.04.008.

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14

Cozzi, Matteo, Alberto Farina, and Enrico Valdinoci. "Monotonicity formulae and classification results for singular, degenerate, anisotropic PDEs." Advances in Mathematics 293 (April 2016): 343–81. http://dx.doi.org/10.1016/j.aim.2016.02.014.

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15

Ma, Li, Xianfa Song, and Lin Zhao. "New monotonicity formulae for semi-linear elliptic and parabolic systems." Chinese Annals of Mathematics, Series B 31, no. 3 (April 20, 2010): 411–32. http://dx.doi.org/10.1007/s11401-008-0282-8.

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16

Li, Jun-Fang. "Eigenvalues and energy functionals with monotonicity formulae under Ricci flow." Mathematische Annalen 338, no. 4 (April 12, 2007): 927–46. http://dx.doi.org/10.1007/s00208-007-0098-y.

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17

Lamberti, Pier Domenico, and Luigi Provenzano. "Neumann to Steklov eigenvalues: asymptotic and monotonicity results." Proceedings of the Royal Society of Edinburgh: Section A Mathematics 147, no. 2 (January 16, 2017): 429–47. http://dx.doi.org/10.1017/s0308210516000214.

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We consider the Steklov eigenvalues of the Laplace operator as limiting Neumann eigenvalues in a problem of mass concentration at the boundary of a ball. We discuss the asymptotic behaviour of the Neumann eigenvalues and find explicit formulae for their derivatives in the limiting problem. We deduce that the Neumann eigenvalues have a monotone behaviour in the limit and that Steklov eigenvalues locally minimize the Neumann eigenvalues.

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18

Li, Junfang. "Evolution of Eigenvalues along Rescaled Ricci Flow." Canadian Mathematical Bulletin 56, no. 1 (March 1, 2013): 127–35. http://dx.doi.org/10.4153/cmb-2011-162-6.

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AbstractIn this paper, we discuss monotonicity formulae of various entropy functionals under various rescaled versions of Ricci flow. As an application, we prove that the lowest eigenvalue of a family of geometric operators -4Δ+kR is monotonic along the normalized Ricci flow for all k≥1 provided the initial manifold has nonpositive total scalar curvature.

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19

CHEN, YONG. "ON THE MONOTONICITY OF FLUCTUATION SPECTRA FOR THREE-STATE MARKOV PROCESSES." Fluctuation and Noise Letters 07, no. 03 (September 2007): L181—L192. http://dx.doi.org/10.1142/s0219477507003830.

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Explicit formulae for correlation functions and fluctuation spectra of the irreducible three-state Markov processes are presented. The necessary and sufficient conditions of existing nonmonotonic fluctuation spectra on [0, +∞) with respect to real functions are given, which reveals that the nonequilibrium flux must be strong enough to produce a peak in the fluctuation spectrum and the monotonicity of fluctuation spectra is related to the time scales of Markov processes.

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20

Milovanović, Gradimir V., and Miodrag M. Spalević. "Monotonicity of the error term in Gauss-Turán quadratures for analytic function." ANZIAM Journal 48, no. 4 (April 2007): 567–81. http://dx.doi.org/10.1017/s1446181100003229.

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AbstractFor Gauss–Turán quadrature formulae with an even weight function on the interval [−1, 1] and functions analytic in regions of the complex plane which contain in their interiors a circle of radius greater than I, the error term is investigated. In some particular cases we prove that the error decreases monotonically to zero. Also, for certain more general cases, we illustrate how to check numerically if this property holds. Some ℓ2-error estimates are considered.

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21

Daduna, Hans, and Ryszard Szekli. "Impact of Routeing on Correlation Strength in Stationary Queueing Network Processes." Journal of Applied Probability 45, no. 3 (September 2008): 846–78. http://dx.doi.org/10.1239/jap/1222441833.

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For exponential open and closed queueing networks, we investigate the internal dependence structure, compare the internal dependence for different networks, and discuss the relation of correlation formulae to the existence of spectral gaps and comparison of asymptotic variances. A central prerequisite for the derived theorems is stochastic monotonicity of the networks. The dependence structure of network processes is described by concordance order with respect to various classes of functions. Different networks with the same first-order characteristics are compared with respect to their second-order properties. If a network is perturbed by changing the routeing in a way which holds the routeing equilibrium fixed, the resulting perturbations of the network processes are evaluated.

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22

Daduna, Hans, and Ryszard Szekli. "Impact of Routeing on Correlation Strength in Stationary Queueing Network Processes." Journal of Applied Probability 45, no. 03 (September 2008): 846–78. http://dx.doi.org/10.1017/s0021900200004745.

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For exponential open and closed queueing networks, we investigate the internal dependence structure, compare the internal dependence for different networks, and discuss the relation of correlation formulae to the existence of spectral gaps and comparison of asymptotic variances. A central prerequisite for the derived theorems is stochastic monotonicity of the networks. The dependence structure of network processes is described by concordance order with respect to various classes of functions. Different networks with the same first-order characteristics are compared with respect to their second-order properties. If a network is perturbed by changing the routeing in a way which holds the routeing equilibrium fixed, the resulting perturbations of the network processes are evaluated.

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23

Conti, Monica, Susanna Terracini, and Gianmaria Verzini. "On a class of optimal partition problems related to the Fu?�k spectrum and to the monotonicity formulae." Calculus of Variations 22, no. 1 (January 2005): 45–72. http://dx.doi.org/10.1007/s00526-004-0266-9.

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24

Bokanowski, Olivier, Athena Picarelli, and Christoph Reisinger. "High-order filtered schemes for time-dependent second order HJB equations." ESAIM: Mathematical Modelling and Numerical Analysis 52, no. 1 (January 2018): 69–97. http://dx.doi.org/10.1051/m2an/2017039.

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In this paper, we present and analyse a class of “filtered” numerical schemes for second order Hamilton–Jacobi–Bellman (HJB) equations. Our approach follows the ideas recently introduced in B.D. Froese and A.M. Oberman, Convergent filtered schemes for the Monge-Ampère partial differential equation, SIAM J. Numer. Anal. 51 (2013) 423–444, and more recently applied by other authors to stationary or time-dependent first order Hamilton–Jacobi equations. For high order approximation schemes (where “high” stands for greater than one), the inevitable loss of monotonicity prevents the use of the classical theoretical results for convergence to viscosity solutions. The work introduces a suitable local modification of these schemes by “filtering” them with a monotone scheme, such that they can be proven convergent and still show an overall high order behaviour for smooth enough solutions. We give theoretical proofs of these claims and illustrate the behaviour with numerical tests from mathematical finance, focussing also on the use of backward differencing formulae for constructing the high order schemes.

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25

Otto, Martin. "An Interpolation Theorem." Bulletin of Symbolic Logic 6, no. 4 (December 2000): 447–62. http://dx.doi.org/10.2307/420966.

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AbstractLyndon's Interpolation Theorem asserts that for any valid implication between two purely relational sentences of first-order logic, there is an interpolant in which each relation symbol appears positively (negatively) only if it appears positively (negatively) in both the antecedent and the succedent of the given implication. We prove a similar, more general interpolation result with the additional requirement that, for some fixed tuple of unary predicates U, all formulae under consideration have all quantifiers explicitly relativised to one of the U. Under this stipulation, existential (universal) quantification over U contributes a positive (negative) occurrence of U.It is shown how this single new interpolation theorem, obtained by a canonical and rather elementary model theoretic proof, unifies a number of related results: the classical characterisation theorems concerning extensions (substructures) with those concerning monotonicity, as well as a many-sorted interpolation theorem focusing on positive vs. negative occurrences of predicates and on existentially vs. universally quantified sorts.

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26

Wan, Ruizhe. "Monotonicity Formula On Cigar Soliton." Journal of Physics: Conference Series 2012, no. 1 (September 1, 2021): 012077. http://dx.doi.org/10.1088/1742-6596/2012/1/012077.

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27

Edquist, Anders, and Arshak Petrosyan. "A parabolic almost monotonicity formula." Mathematische Annalen 341, no. 2 (December 12, 2007): 429–54. http://dx.doi.org/10.1007/s00208-007-0195-y.

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28

Chai, Xiaoxiang. "Willmore type inequality using monotonicity formulas." Pacific Journal of Mathematics 307, no. 1 (August 8, 2020): 53–62. http://dx.doi.org/10.2140/pjm.2020.307.53.

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29

Blanchette, Jasmin Christian, and Alexander Krauss. "Monotonicity Inference for Higher-Order Formulas." Journal of Automated Reasoning 47, no. 4 (August 13, 2011): 369–98. http://dx.doi.org/10.1007/s10817-011-9234-1.

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30

Garza-Hume, C. E. "Liquid crystals and the monotonicity formula." Physica D: Nonlinear Phenomena 114, no. 1-2 (March 1998): 172–80. http://dx.doi.org/10.1016/s0167-2789(97)00180-2.

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31

Xing, Qiao Fang, and Xiang Gao. "F Functional and the First Eigenvalue for Quasi-Einstein Metrics." Applied Mechanics and Materials 475-476 (December 2013): 1079–83. http://dx.doi.org/10.4028/www.scientific.net/amm.475-476.1079.

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In this paper, we deal with the monotonicity properties of the first eigenvalue of the Laplacian operator. Firstly, by using the monotonicity formula of theFfunctional, we derive a monotonicity formula of the first eigenvalue of the Laplacian operator. Based on this, we also prove an exponential decreasing property of the first eigenvalue.

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32

Borovcanin, Momcilo. "Some consequence relations on propositional formulas." Serbian Journal of Electrical Engineering 8, no. 1 (2011): 9–15. http://dx.doi.org/10.2298/sjee1101009b.

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Consequence relations on propositional formulas are binary relations on propositional formulas that represent certain types of entailment - formal or semi-formal derivation of conclusion from a certain set of premises. Some of well known examples are classical implication (standard logical entailment), preference relations (i.e. relations that satisfy Reflexivity, Left logical equivalence, Right weakening, And, Or and Cautious monotonicity) rational relations (i.e. preference relations that also satisfy rational monotonicity), consequence relations (prime examples are qualitative possibilities and necessities) etc. More than two decades various consequence relations are used in automated decision making, product control, risk assessment and so on. The aim of this paper is to give a short overview of the most prominent examples of consequence relations.

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33

Spolaor, Luca. "Monotonicity Formulas in the Calculus of Variation." Notices of the American Mathematical Society 69, no. 10 (November 1, 2022): 1. http://dx.doi.org/10.1090/noti2569.

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34

Alhejji, Mohammad A., and Graeme Smith. "Monotonicity Under Local Operations: Linear Entropic Formulas." IEEE Transactions on Information Theory 66, no. 8 (August 2020): 5055–60. http://dx.doi.org/10.1109/tit.2020.2986728.

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35

Wang, Lin Feng. "Monotonicity formulas via the Bakry–Émery curvature." Nonlinear Analysis: Theory, Methods & Applications 89 (September 2013): 230–41. http://dx.doi.org/10.1016/j.na.2013.05.018.

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36

Hamilton, Richard S. "Monotonicity formulas for parabolic flows on manifolds." Communications in Analysis and Geometry 1, no. 1 (1993): 127–37. http://dx.doi.org/10.4310/cag.1993.v1.n1.a7.

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37

Liu, Yongping. "Higher monotonicity properties of normalized Bessel functions." International Journal of Wavelets, Multiresolution and Information Processing 12, no. 05 (September 2014): 1461007. http://dx.doi.org/10.1142/s0219691314610074.

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Denote by Jν the Bessel function of the first kind of order ν and μν,k is its kth positive zero. For ν > ½, a theorem of Lorch, Muldoon and Szegö states that the sequence [Formula: see text] is decreasing, another theorem of theirs states that the sequence [Formula: see text] has higher monotonicity properties. In the present paper, we proved that when ν > ½ the sequence [Formula: see text] has higher monotonicity properties and the properties imply those of the sequence of the local maxima of the function x-ν+1|Jν-1(x)|, x ∈ (0, ∞), i.e. the sequence [Formula: see text] has higher monotonicity properties.

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38

Apushkinskaya, D. E., and N. N. Uraltseva. "Monotonicity Formula for a Problem with Hysteresis." Doklady Mathematics 97, no. 1 (January 2018): 49–51. http://dx.doi.org/10.1134/s1064562418010167.

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39

Yamada, Sumio. "A dual monotonicity formula for harmonic mappings." Calculus of Variations and Partial Differential Equations 18, no. 2 (October 1, 2003): 181–88. http://dx.doi.org/10.1007/s00526-002-0187-4.

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40

Angelsberg, Gilles. "A monotonicity formula for stationary biharmonic maps." Mathematische Zeitschrift 252, no. 2 (August 16, 2005): 287–93. http://dx.doi.org/10.1007/s00209-005-0848-z.

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41

Agostiniani, Virginia, Mattia Fogagnolo, and Lorenzo Mazzieri. "Minkowski Inequalities via Nonlinear Potential Theory." Archive for Rational Mechanics and Analysis 244, no. 1 (February 11, 2022): 51–85. http://dx.doi.org/10.1007/s00205-022-01756-6.

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AbstractIn this paper, we prove an extended version of the Minkowski Inequality, holding for any smooth bounded set $$\Omega \subset \mathbb {R}^n$$ Ω ⊂ R n , $$n\ge 3$$ n ≥ 3 . Our proof relies on the discovery of effective monotonicity formulas holding along the level set flow of the p-capacitary potentials associated with $$\Omega $$ Ω , for every p sufficiently close to 1. These formulas also testify the existence of a link between the monotonicity formulas derived by Colding and Minicozzi for the level set flow of Green’s functions and the monotonicity formulas employed by Huisken, Ilmanen and several other authors in studying the geometric implications of the Inverse Mean Curvature Flow. In dimension $$n\ge 8$$ n ≥ 8 , our conclusions are stronger than the ones obtained so far through the latter mentioned technique.

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42

Branding, Volker. "Nonlinear Dirac Equations, Monotonicity Formulas and Liouville Theorems." Communications in Mathematical Physics 372, no. 3 (November 13, 2019): 733–67. http://dx.doi.org/10.1007/s00220-019-03608-z.

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Abstract We study the qualitative behavior of nonlinear Dirac equations arising in quantum field theory on complete Riemannian manifolds. In particular, we derive monotonicity formulas and Liouville theorems for solutions of these equations. Finally, we extend our analysis to Dirac-harmonic maps with curvature term.

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43

Ecker, Klaus. "Local monotonicity formulas for some nonlinear diffusion equations." Calculus of Variations and Partial Differential Equations 23, no. 1 (May 2005): 67–81. http://dx.doi.org/10.1007/s00526-004-0290-9.

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44

Focardi, M., M. S. Gelli, and E. Spadaro. "Monotonicity formulas for obstacle problems with Lipschitz coefficients." Calculus of Variations and Partial Differential Equations 54, no. 2 (February 20, 2015): 1547–73. http://dx.doi.org/10.1007/s00526-015-0835-0.

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45

Song, Bingyu, Guofang Wei, and Guoqiang Wu. "Monotonicity Formulas for the Bakry–Emery Ricci Curvature." Journal of Geometric Analysis 25, no. 4 (September 4, 2014): 2716–35. http://dx.doi.org/10.1007/s12220-014-9533-y.

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46

Eberhard, A. C., and Hossein Mohebi. "Maximal Abstract Monotonicity and Generalized Fenchel’s Conjugation Formulas." Set-Valued and Variational Analysis 18, no. 1 (November 11, 2009): 79–108. http://dx.doi.org/10.1007/s11228-009-0124-1.

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47

Ecker, Klaus. "A Local Monotonicity Formula for Mean Curvature Flow." Annals of Mathematics 154, no. 2 (September 2001): 503. http://dx.doi.org/10.2307/3062105.

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48

Lee, Paul W. Y. "Generalized Li−Yau estimates and Huisken’s monotonicity formula." ESAIM: Control, Optimisation and Calculus of Variations 23, no. 3 (April 10, 2017): 827–50. http://dx.doi.org/10.1051/cocv/2016015.

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49

Guo, Songbai, Youjian Shen, and Binbin Shi. "Monotonicity and Boundedness of Remainder of Stirling's Formula." Journal of Interdisciplinary Mathematics 17, no. 4 (July 4, 2014): 345–53. http://dx.doi.org/10.1080/09720502.2014.932118.

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50

Ecker, Klaus. "A formula relating entropy monotonicity to Harnack inequalities." Communications in Analysis and Geometry 15, no. 5 (2007): 1025–61. http://dx.doi.org/10.4310/cag.2007.v15.n5.a5.

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