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Journal articles on the topic 'Divergence form operators'

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Author: Grafiati

Published: 10 December 2022

Last updated: 28 January 2023

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1

Milakis, Emmanouil, and Tatiana Toro. "Divergence form operators in Reifenberg flat domains." Mathematische Zeitschrift 264, no. 1 (November 14, 2008): 15–41. http://dx.doi.org/10.1007/s00209-008-0450-2.

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2

Barlow, Martin T., and Richard F. Bass. "Divergence Form Operators on Fractal-like Domains." Journal of Functional Analysis 175, no. 1 (August 2000): 214–47. http://dx.doi.org/10.1006/jfan.2000.3597.

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3

Boccardo, L., and B. Dacorogna. "Monotonicity of certain differential operators in divergence form." Manuscripta Mathematica 64, no. 2 (June 1989): 253–60. http://dx.doi.org/10.1007/bf01160123.

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4

Barlow, Martin T. "On the Liouville Property for Divergence Form Operators." Canadian Journal of Mathematics 50, no. 3 (June 1, 1998): 487–96. http://dx.doi.org/10.4153/cjm-1998-026-9.

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AbstractIn this paper we construct a bounded strictly positive function σ such that the Liouville property fails for the divergence form operator L= ▽ (σ2▽). Since in addition Δσ/σ is bounded, this example also gives a negative answer to a problem of Berestycki, Caffarelli and Nirenberg concerning linear Schrödinger operators.

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5

Song, Liang, and Ming Xu. "VMO spaces associated with divergence form elliptic operators." Mathematische Zeitschrift 269, no. 3-4 (September 3, 2010): 927–43. http://dx.doi.org/10.1007/s00209-010-0774-6.

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6

Maekawa, Yasunori, and Hideyuki Miura. "On domain of Poisson operators and factorization for divergence form elliptic operators." manuscripta mathematica 152, no. 3-4 (June 13, 2016): 459–512. http://dx.doi.org/10.1007/s00229-016-0858-7.

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7

ter Elst, A. F. M., and Derek W. Robinson. "High order divergence-form elliptic operators on Lie groups." Bulletin of the Australian Mathematical Society 55, no. 2 (April 1997): 335–48. http://dx.doi.org/10.1017/s0004972700034006.

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8

Okazawa, Noboru. "Sectorialness of second order elliptic operators in divergence form." Proceedings of the American Mathematical Society 113, no. 3 (March 1, 1991): 701. http://dx.doi.org/10.1090/s0002-9939-1991-1072347-4.

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9

Rozkosz, Andrzej. "Weak convergence of diffusions corresponding to divergence form operators." Stochastics and Stochastic Reports 57, no. 1-2 (August 1996): 129–57. http://dx.doi.org/10.1080/17442509608834055.

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10

Miyazaki, Yoichi. "Schauder theory for Dirichlet elliptic operators in divergence form." Journal of Evolution Equations 13, no. 2 (March 27, 2013): 443–80. http://dx.doi.org/10.1007/s00028-013-0186-2.

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11

Egert, Moritz. "On p-elliptic divergence form operators and holomorphic semigroups." Journal of Evolution Equations 20, no. 3 (October 8, 2019): 705–24. http://dx.doi.org/10.1007/s00028-019-00537-1.

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12

Rozkosz, Andrzej. "Stochastic representation of diffusions corresponding to divergence form operators." Stochastic Processes and their Applications 63, no. 1 (October 1996): 11–33. http://dx.doi.org/10.1016/0304-4149(96)00059-2.

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13

Khenissy, Saïma, Yomna Rébaï, and Dong Ye. "Expansion of the Green's function for divergence form operators." Comptes Rendus Mathematique 348, no. 15-16 (August 2010): 891–96. http://dx.doi.org/10.1016/j.crma.2010.06.024.

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14

Elst, A. F. M. ter, Derek W. Robinson, and Adam Sikora. "On second-order periodic elliptic operators in divergence form." Mathematische Zeitschrift 238, no. 3 (November 1, 2001): 569–637. http://dx.doi.org/10.1007/s002090100268.

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15

Bass, Richard F., and Krzysztof Burdzy. "The Boundary Harnack Principle for Non-Divergence form Elliptic Operators." Journal of the London Mathematical Society 50, no. 1 (August 1994): 157–69. http://dx.doi.org/10.1112/jlms/50.1.157.

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16

Bonfiglioli, Andrea, Ermanno Lanconelli, and Francesco Uguzzoni. "Fundamental solutions for non-divergence form operators on stratified groups." Transactions of the American Mathematical Society 356, no. 7 (October 21, 2003): 2709–37. http://dx.doi.org/10.1090/s0002-9947-03-03332-4.

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17

Bonfiglioli, Andrea, and Francesco Uguzzoni. "Harnack inequality for non-divergence form operators on stratified groups." Transactions of the American Mathematical Society 359, no. 6 (January 19, 2007): 2463–81. http://dx.doi.org/10.1090/s0002-9947-07-04273-0.

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18

ARENA, ORAZIO, and CRISTINA GIANNOTTI. "ELLIPTIC EXTENSIONS IN THE DISK WITH OPERATORS IN DIVERGENCE FORM." Bulletin of the Australian Mathematical Society 88, no. 1 (August 20, 2012): 51–55. http://dx.doi.org/10.1017/s000497271200069x.

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AbstractLet $\varphi _0$ and $\varphi _1$ be regular functions on the boundary $\partial D$ of the unit disk $D$ in $\mathbb {R}^2$, such that $\int _{0}^{2\pi }\varphi _1\,d\theta =0$ and $\int _{0}^{2\pi }\sin \theta (\varphi _1-\varphi _0)\,d\theta =0$. It is proved that there exist a linear second-order uniformly elliptic operator $L$ in divergence form with bounded measurable coefficients and a function $u$ in $W^{1,p}(D)$, $1 \lt p \lt 2$, such that $Lu=0$ in $D$ and with $u|_{\partial D}= \varphi _0$ and the conormal derivative $\partial u/\partial N|_{\partial D}=\varphi _1$.

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19

Bonfiglioli, Andrea, Ermanno Lanconelli, and Francesco Uguzzoni. "Levi’s parametrix for some sub-elliptic non-divergence form operators." Electronic Research Announcements of the American Mathematical Society 9, no. 2 (January 31, 2003): 10–18. http://dx.doi.org/10.1090/s1079-6762-03-00107-0.

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20

Stroock, Daniel W. "Non-divergence form operators and variations on Yau's explosion criterion." Journal of Fourier Analysis and Applications 4, no. 4-5 (July 1998): 565–74. http://dx.doi.org/10.1007/bf02498225.

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21

Mihăilescu, Mihai. "Classification of isolated singularities for nonhomogeneous operators in divergence form." Journal of Functional Analysis 268, no. 8 (April 2015): 2336–55. http://dx.doi.org/10.1016/j.jfa.2015.01.016.

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22

Saloff-Coste, L. "Parabolic Harnack inequality for divergence form second order differential operators." Potential Analysis 4, no. 4 (August 1995): 429–67. http://dx.doi.org/10.1007/bf01053457.

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23

Arlinskii, Yury, and Yury Kovalev. "Operators in divergence form and their Friedrichs and Krein extensions." Opuscula Mathematica 31, no. 4 (2011): 501. http://dx.doi.org/10.7494/opmath.2011.31.4.501.

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24

Hofmann, Steve, and Svitlana Mayboroda. "Hardy and BMO spaces associated to divergence form elliptic operators." Mathematische Annalen 344, no. 1 (October 31, 2008): 37–116. http://dx.doi.org/10.1007/s00208-008-0295-3.

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25

Jiang, Renjin, and Dachun Yang. "New Orlicz–Hardy spaces associated with divergence form elliptic operators." Journal of Functional Analysis 258, no. 4 (February 2010): 1167–224. http://dx.doi.org/10.1016/j.jfa.2009.10.018.

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26

Bessa, Gregório P., Luquésio P. Jorge, Barnabé P. Lima, and José F. Montenegro. "Fundamental tone estimates for elliptic operators in divergence form and geometric applications." Anais da Academia Brasileira de Ciências 78, no. 3 (September 2006): 391–404. http://dx.doi.org/10.1590/s0001-37652006000300001.

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We establish a method for giving lower bounds for the fundamental tone of elliptic operators in divergence form in terms of the divergence of vector fields. We then apply this method to the Lr operator associated to immersed hypersurfaces with locally bounded (r + 1)-th mean curvature Hr + 1 of the space forms Nn+ 1(c) of constant sectional curvature c. As a corollary we give lower bounds for the extrinsic radius of closed hypersurfaces of Nn+ 1(c) with Hr + 1 > 0 in terms of the r-th and (r + 1)-th mean curvatures. Finally we observe that bounds for the Laplace eigenvalues essentially bound the eigenvalues of a self-adjoint elliptic differential operator in divergence form. This allows us to show that Cheeger's constant gives a lower bounds for the first nonzero Lr-eigenvalue of a closed hypersurface of Nn+ 1(c).

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27

Auscher, Pascal, Moritz Egert, and Kaj Nyström. "The Dirichlet problem for second order parabolic operators in divergence form." Journal de l’École polytechnique — Mathématiques 5 (2018): 407–41. http://dx.doi.org/10.5802/jep.74.

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28

Li, Peter, and Jiaping Wang. "Polynomial growth solutions of uniformly elliptic operators of non-divergence form." Proceedings of the American Mathematical Society 129, no. 12 (May 10, 2001): 3691–99. http://dx.doi.org/10.1090/s0002-9939-01-06167-6.

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29

Klimsiak, Tomasz. "On Time-Dependent Functionals of Diffusions Corresponding to Divergence Form Operators." Journal of Theoretical Probability 26, no. 2 (September 28, 2011): 437–73. http://dx.doi.org/10.1007/s10959-011-0381-4.

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30

Du, Feng, Chuanxi Wu, and Guanghan Li. "Estimates for eigenvalues of fourth-order elliptic operators in divergence form." Bulletin of the Brazilian Mathematical Society, New Series 46, no. 3 (September 2015): 437–59. http://dx.doi.org/10.1007/s00574-015-0099-5.

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31

Quastel, J., and S. R. S. Varadhan. "Diffusion semigroups and diffusion processes corresponding to degenerate divergence form operators." Communications on Pure and Applied Mathematics 50, no. 7 (July 1997): 667–705. http://dx.doi.org/10.1002/(sici)1097-0312(199707)50:7<667::aid-cpa3>3.0.co;2-5.

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32

Auscher, Pascal, and Moritz Egert. "On non-autonomous maximal regularity for elliptic operators in divergence form." Archiv der Mathematik 107, no. 3 (July 4, 2016): 271–84. http://dx.doi.org/10.1007/s00013-016-0934-y.

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33

Jiang, Renjin, and Dachun Yang. "Generalized Vanishing Mean Oscillation Spaces Associated with Divergence Form Elliptic Operators." Integral Equations and Operator Theory 67, no. 1 (April 13, 2010): 123–49. http://dx.doi.org/10.1007/s00020-010-1774-y.

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34

Lim, Nancy L. "TheLpDirichlet Problem for Divergence Form Elliptic Operators with Non-smooth Coefficients." Journal of Functional Analysis 138, no. 2 (June 1996): 502–43. http://dx.doi.org/10.1006/jfan.1996.0074.

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35

TANG, LIN. "WEIGHTED SOLVABILITY FOR PARABOLIC EQUATIONS WITH PARTIALLY BMO COEFFICIENTS AND ITS APPLICATIONS." Journal of the Australian Mathematical Society 96, no. 3 (June 2014): 396–428. http://dx.doi.org/10.1017/s1446788714000020.

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AbstractWe consider the weighted $L_p$ solvability for divergence and nondivergence form parabolic equations with partially bounded mean oscillation (BMO) coefficients and certain positive potentials. As an application, global regularity in Morrey spaces for divergence form parabolic operators with partially BMO coefficients on a bounded domain is established.

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36

Tan, Shenyang, Tiren Huang, and Wenbin Zhang. "Estimates for Eigenvalues of the Elliptic Operator in Divergence Form on Riemannian Manifolds." Advances in Mathematical Physics 2015 (2015): 1–8. http://dx.doi.org/10.1155/2015/387953.

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We investigate the Dirichlet weighted eigenvalue problem of the elliptic operator in divergence form on compact Riemannian manifolds(M,g,e-ϕdv). We establish a Yang-type inequality of this problem. We also get universal inequalities for eigenvalues of elliptic operators in divergence form on compact domains of complete submanifolds admitting special functions which include the Hadamard manifolds with Ricci curvature bounded below and any complete manifolds admitting eigenmaps to a sphere.

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37

Gomes, José N. V., and Juliana F. R. Miranda. "Eigenvalue estimates for a class of elliptic differential operators in divergence form." Nonlinear Analysis 176 (November 2018): 1–19. http://dx.doi.org/10.1016/j.na.2018.06.006.

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38

Frentz, Marie, Elin Götmark, and Kaj Nyström. "The obstacle problem for parabolic non-divergence form operators of Hörmander type." Journal of Differential Equations 252, no. 9 (May 2012): 5002–41. http://dx.doi.org/10.1016/j.jde.2012.01.032.

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39

Rosén, Andreas. "Square function and maximal function estimates for operators beyond divergence form equations." Journal of Evolution Equations 13, no. 3 (June 9, 2013): 651–74. http://dx.doi.org/10.1007/s00028-013-0195-1.

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40

Miyazaki, Yoichi. "The Lp theory of divergence form elliptic operators under the Dirichlet condition." Journal of Differential Equations 215, no. 2 (August 2005): 320–56. http://dx.doi.org/10.1016/j.jde.2004.10.014.

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41

Miyazaki, Yoichi. "Higher order elliptic operators of divergence form in C1 or Lipschitz domains." Journal of Differential Equations 230, no. 1 (November 2006): 174–95. http://dx.doi.org/10.1016/j.jde.2006.07.024.

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42

Lejay, Antoine. "Homogenization of divergence-form operators with lower-order terms in random media." Probability Theory and Related Fields 120, no. 2 (June 2001): 255–76. http://dx.doi.org/10.1007/pl00008783.

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43

Aryal, Ashok, and Ivan Blank. "Geometry of Mean Value Sets for General Divergence Form Uniformly Elliptic Operators." Potential Analysis 50, no. 1 (December 15, 2017): 43–54. http://dx.doi.org/10.1007/s11118-017-9672-4.

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44

Ros-Oton, Xavier, and Joaquim Serra. "The Boundary Harnack Principle for Nonlocal Elliptic Operators in Non-divergence Form." Potential Analysis 51, no. 3 (June 15, 2018): 315–31. http://dx.doi.org/10.1007/s11118-018-9713-7.

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45

Francfort, Gilles A., François Murat, and Luc Tartar. "Homogenization of monotone operators in divergence form with x-dependent multivalued graphs." Annali di Matematica Pura ed Applicata 188, no. 4 (February 10, 2009): 631–52. http://dx.doi.org/10.1007/s10231-009-0094-9.

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46

do Carmo, Manfredo P., Qiaoling Wang, and Changyu Xia. "Inequalities for eigenvalues of elliptic operators in divergence form on Riemannian manifolds." Annali di Matematica Pura ed Applicata 189, no. 4 (February 9, 2010): 643–60. http://dx.doi.org/10.1007/s10231-010-0129-2.

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47

Dragičević, Oliver, and Alexander Volberg. "Bilinear embedding for real elliptic differential operators in divergence form with potentials." Journal of Functional Analysis 261, no. 10 (November 2011): 2816–28. http://dx.doi.org/10.1016/j.jfa.2011.07.013.

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48

Xie, Peizhu, and Ruming Gong. "Commutators with Lipschitz Functions and Nonintegral Operators." Journal of Applied Mathematics 2013 (2013): 1–8. http://dx.doi.org/10.1155/2013/178961.

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LetTbe a singular nonintegral operator; that is, it does not have an integral representation by a kernel with size estimates, even rough. In this paper, we consider the boundedness of commutators withTand Lipschitz functions. Applications include spectral multipliers of self-adjoint, positive operators, Riesz transforms of second-order divergence form operators, and fractional power of elliptic operators.

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49

Cialdea, Alberto, Vita Leonessa, and Angelica Malaspina. "The Dirichlet Problem for Second-Order Divergence Form Elliptic Operators with Variable Coefficients: The Simple Layer Potential Ansatz." Abstract and Applied Analysis 2015 (2015): 1–11. http://dx.doi.org/10.1155/2015/276810.

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We investigate the Dirichlet problem related to linear elliptic second-order partial differential operators with smooth coefficients in divergence form in bounded connected domains ofRm(m≥3) with Lyapunov boundary. In particular, we show how to represent the solution in terms of a simple layer potential. We use an indirect boundary integral method hinging on the theory of reducible operators and the theory of differential forms.

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50

Cakoni, Fioralba, and Jingni Xiao. "On corner scattering for operators of divergence form and applications to inverse scattering." Communications in Partial Differential Equations 46, no. 3 (March 4, 2021): 413–41. http://dx.doi.org/10.1080/03605302.2020.1843489.

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