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Journal articles on the topic 'Isoperimetric problems'

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Published: 28 June 2021
Last updated: 8 February 2022

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1

Petty, C. M. "AFFINE ISOPERIMETRIC PROBLEMS." Annals of the New York Academy of Sciences 440, no. 1 Discrete Geom (May 1985): 113–27. http://dx.doi.org/10.1111/j.1749-6632.1985.tb14545.x.

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2

Apostol, Tom M., and Mamikon A. Mnatsakanian. "Isoperimetric and Isoparametric Problems." American Mathematical Monthly 111, no. 2 (February 2004): 118. http://dx.doi.org/10.2307/4145213.

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3

Apostol, Tom M., and Mamikon A. Mnatsakanian. "Isoperimetric and Isoparametric Problems." American Mathematical Monthly 111, no. 2 (February 2004): 118–36. http://dx.doi.org/10.1080/00029890.2004.11920056.

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4

Tóth, L. Fejes. "Isoperimetric problems for tilings." Mathematika 32, no. 1 (June 1985): 10–15. http://dx.doi.org/10.1112/s0025579300010792.

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5

BOLLOBÁS, BÉLA, and IMRE LEADER. "Isoperimetric Problems for r-sets." Combinatorics, Probability and Computing 13, no. 2 (March 2004): 277–79. http://dx.doi.org/10.1017/s0963548304006078.

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6

Tóth, L. Fejes. "Isoperimetric problems for tilings, corrigendum." Mathematika 33, no. 2 (December 1986): 189–91. http://dx.doi.org/10.1112/s0025579300011177.

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7

Siegel, Jerrold, and Frank Williams. "Uniform bounds for isoperimetric problems." Proceedings of the American Mathematical Society 107, no. 2 (February 1, 1989): 459. http://dx.doi.org/10.1090/s0002-9939-1989-0984815-2.

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8

Ritoré, Manuel, and Antonio Ros. "Some updates on isoperimetric problems." Mathematical Intelligencer 24, no. 3 (June 2002): 9–14. http://dx.doi.org/10.1007/bf03024725.

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9

Clarenz, Ulrich, and Heiko von der Mosel. "Isoperimetric inequalities for parametric variational problems." Annales de l'Institut Henri Poincare (C) Non Linear Analysis 19, no. 5 (2002): 617–29. http://dx.doi.org/10.1016/s0294-1449(02)00096-3.

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10

Demyanov, V. F., and G. Sh Tamasyan. "Exact penalty functions in isoperimetric problems." Optimization 60, no. 1-2 (January 2011): 153–77. http://dx.doi.org/10.1080/02331934.2010.534166.

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11

Ahlbrandt, Calvin D., and Betty Jean Harmsen. "Discrete versions of continuous isoperimetric problems." Journal of Difference Equations and Applications 3, no. 5-6 (January 1998): 449–62. http://dx.doi.org/10.1080/10236199708808114.

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12

Rizcallah, Joseph A. "Isoperimetric Triangles." Mathematics Teacher 111, no. 1 (September 2017): 70–74. http://dx.doi.org/10.5951/mathteacher.111.1.0070.

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The isoperimetric problem is a well-known problem in geometry, and it has a long and rich history (Blasjo 2005). In the plane, the isoperimetric problem consists of finding the simple closed curve of a given perimeter that encloses the greatest area, with the circle being the famous solution. Attempts to solve the isoperimetric problem, as well as other analogous problems in calculus and physics, were undertaken by many great mathematicians in the past whose work ultimately laid the foundation for the elegant branch of analysis known today as the calculus of variations.
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13

Lucia, Marcello. "Isoperimetric profile and uniqueness for Neumann problems." Annales de l'Institut Henri Poincare (C) Non Linear Analysis 26, no. 1 (January 2009): 81–100. http://dx.doi.org/10.1016/j.anihpc.2007.07.002.

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14

Curtis, John P. "Complementary Extremum Principles for Isoperimetric Optimization Problems." Optimization and Engineering 5, no. 4 (December 2004): 417–30. http://dx.doi.org/10.1023/b:opte.0000042033.33845.4c.

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15

Viterbo, Claude. "Metric and isoperimetric problems in symplectic geometry." Journal of the American Mathematical Society 13, no. 2 (January 31, 2000): 411–31. http://dx.doi.org/10.1090/s0894-0347-00-00328-3.

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16

Caputo, M. R. "Economic Characterization of Reciprocal Isoperimetric Control Problems." Journal of Optimization Theory and Applications 98, no. 2 (August 1998): 325–50. http://dx.doi.org/10.1023/a:1022685417012.

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17

Cañete, Antonio, Michele Miranda, and Davide Vittone. "Some Isoperimetric Problems in Planes with Density." Journal of Geometric Analysis 20, no. 2 (September 30, 2009): 243–90. http://dx.doi.org/10.1007/s12220-009-9109-4.

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18

Ezz–Eldien, Samer S., Ali H. Bhrawy, and Ahmed A. El–Kalaawy. "Direct numerical method for isoperimetric fractional variational problems based on operational matrix." Journal of Vibration and Control 24, no. 14 (April 2, 2017): 3063–76. http://dx.doi.org/10.1177/1077546317700344.

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In this paper, we applied a direct method for a solution of isoperimetric fractional variational problems. We use shifted Legendre orthonormal polynomials as basis function of operational matrices of fractional differentiation and fractional integration in combination with the Lagrange multipliers technique for converting such isoperimetric fractional variational problems into solving a system of algebraic equations. Also, we show the convergence analysis of the presented technique and introduce some test problems with comparisons between our numerical results with those introduced using different methods.
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19

Krizek, Jan, Josef Mikes, Patrik Peska, and Lenka Ryparova. "Extremals and Isoperimetric Extremals of the Rotations in the Plane." Geometry, Integrability and Quantization 22 (2021): 136–41. http://dx.doi.org/10.7546/giq-22-2021-136-141.

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In the paper we study the extremals and isoperimetric extremals of the rotations in the plane. We found that extremals of the rotations in the plane are arbitrary curves. By studying the Euler-Poisson equations for extended variational problems, we found that the isoperimetric extremals of the rotations in the Euclidian plane are straight lines.
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20

Bezrukov, Sergei L., and Oriol Serra. "A local–global principle for vertex-isoperimetric problems." Discrete Mathematics 257, no. 2-3 (November 2002): 285–309. http://dx.doi.org/10.1016/s0012-365x(02)00431-4.

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21

Caputo, M. R. "Economic Characterization of Reciprocal Isoperimetric Control Problems Revisited." Journal of Optimization Theory and Applications 101, no. 3 (June 1999): 723–30. http://dx.doi.org/10.1023/a:1021750406667.

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22

Almeida, Ricardo, and Delfim F. M. Torres. "Isoperimetric Problems on Time Scales with Nabla Derivatives." Journal of Vibration and Control 15, no. 6 (March 31, 2009): 951–58. http://dx.doi.org/10.1177/1077546309103268.

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23

Daneshgar, Amir, and Ramin Javadi. "On the complexity of isoperimetric problems on trees." Discrete Applied Mathematics 160, no. 1-2 (January 2012): 116–31. http://dx.doi.org/10.1016/j.dam.2011.08.015.

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24

Rosenblueth, Javier F. "A New Notion of Conjugacy for Isoperimetric Problems." Applied Mathematics and Optimization 50, no. 3 (September 10, 2004): 209–28. http://dx.doi.org/10.1007/s00245-004-0800-3.

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25

PRUSINSKA, AGNIESZKA, EWA SZCZEPANIK, and ALEXEY A. TRETYAKOV. "High-order optimality conditions for degenerate variational problems." Carpathian Journal of Mathematics 30, no. 3 (2014): 387–94. http://dx.doi.org/10.37193/cjm.2014.03.03.

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The paper is devoted to the class of singular calculus of variations problems with constraints which are not regular mappings at the solution point. Methods of the p-regularity theory are used for investigation of isoperimetric and Lagrange singular problems. Necessary conditions for optimality in p-regular calculus of variations problem are presented.
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26

Urziceanu, Silviu-Aurelian. "Necessary Optimality Conditions in Isoperimetric Constrained Optimal Control Problems." Symmetry 11, no. 11 (November 7, 2019): 1380. http://dx.doi.org/10.3390/sym11111380.

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In this paper, we focus on a new class of optimal control problems governed by a simple integral cost functional and isoperimetric-type constraints (constant level sets of some simple integral functionals). By using the notions of a variational differential system and adjoint equation, necessary optimality conditions are established for a feasible solution in the considered optimization problem. More precisely, under simplified hypotheses and using a modified Legendrian duality, we establish a maximum principle for the considered optimization problem.
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27

Pacella, Filomena, and Giulio Tralli. "Isoperimetric cones and minimal solutions of partial overdetermined problems." Publicacions Matemàtiques 65 (January 1, 2021): 61–81. http://dx.doi.org/10.5565/publmat6512102.

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28

Hamel, François, Nikolai Nadirashvili, and Emmanuel Russ. "Rearrangement inequalities and applications to isoperimetric problems for eigenvalues." Annals of Mathematics 174, no. 2 (September 1, 2011): 647–755. http://dx.doi.org/10.4007/annals.2011.174.2.1.

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29

Bezrukov, Sergei L., and Robert Elsässer. "Edge-isoperimetric problems for cartesian powers of regular graphs." Theoretical Computer Science 307, no. 3 (October 2003): 473–92. http://dx.doi.org/10.1016/s0304-3975(03)00232-9.

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30

Becerril, Jorge, and Karla Cortez. "Normality and Uniqueness of Multipliers in Isoperimetric Control Problems." Journal of Optimization Theory and Applications 182, no. 3 (April 3, 2019): 947–64. http://dx.doi.org/10.1007/s10957-019-01515-w.

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31

Maggi, F. "Some methods for studying stability in isoperimetric type problems." Bulletin of the American Mathematical Society 45, no. 3 (April 8, 2008): 367–408. http://dx.doi.org/10.1090/s0273-0979-08-01206-8.

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32

Cianchi, Andrea. "Moser-Trudinger inequalities without boundary conditions and isoperimetric problems." Indiana University Mathematics Journal 54, no. 3 (2005): 669–706. http://dx.doi.org/10.1512/iumj.2005.54.2589.

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33

Cabré, Xavier, Xavier Ros-Oton, and Joaquim Serra. "Euclidean balls solve some isoperimetric problems with nonradial weights." Comptes Rendus Mathematique 350, no. 21-22 (November 2012): 945–47. http://dx.doi.org/10.1016/j.crma.2012.10.031.

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34

Caputo, Michael R. "A unified view of ostensibly disparate isoperimetric variational problems." Applied Mathematics Letters 22, no. 3 (March 2009): 332–35. http://dx.doi.org/10.1016/j.aml.2008.04.004.

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35

Stammbach, Urs. "A Letter of Hermann Amandus Schwarz on Isoperimetric Problems." Mathematical Intelligencer 34, no. 1 (February 4, 2012): 44–51. http://dx.doi.org/10.1007/s00283-011-9267-7.

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36

Kannan, R., L. Lovász, and M. Simonovits. "Isoperimetric problems for convex bodies and a localization lemma." Discrete & Computational Geometry 13, no. 3-4 (June 1995): 541–59. http://dx.doi.org/10.1007/bf02574061.

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37

Treanţă, Savin. "On well-posed isoperimetric-type constrained variational control problems." Journal of Differential Equations 298 (October 2021): 480–99. http://dx.doi.org/10.1016/j.jde.2021.07.013.

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38

Treanţă, Savin. "On a Class of Isoperimetric Constrained Controlled Optimization Problems." Axioms 10, no. 2 (June 3, 2021): 112. http://dx.doi.org/10.3390/axioms10020112.

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In this paper, we investigate the Lagrange dynamics generated by a class of isoperimetric constrained controlled optimization problems involving second-order partial derivatives and boundary conditions. More precisely, we derive necessary optimality conditions for the considered class of variational control problems governed by path-independent curvilinear integral functionals. Moreover, the theoretical results presented in the paper are accompanied by an illustrative example. Furthermore, an algorithm is proposed to emphasize the steps to be followed to solve a control problem such as the one studied in this paper.
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39

Pitea, Ariana. "A Study of Some General Problems of Dieudonné-Rashevski Type." Abstract and Applied Analysis 2012 (2012): 1–11. http://dx.doi.org/10.1155/2012/592804.

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We use a method of investigation based on employing adequate variational calculus techniques in the study of some generalized Dieudonné-Rashevski problems. This approach allows us to state and prove optimality conditions for such kind of vector multitime variational problems, with mixed isoperimetric constraints. We state and prove efficiency conditions and develop a duality theory.
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40

Klimov, Vladimir S. "Isoperimetric and Functional Inequalities." Modeling and Analysis of Information Systems 25, no. 3 (June 30, 2018): 331–42. http://dx.doi.org/10.18255/1818-1015-2018-3-331-342.

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We establish lower estimates for an integral functional$$\int\limits_\Omega f(u(x), \nabla u(x)) \, dx ,$$where \(\Omega\) -- a bounded domain in \(\mathbb{R}^n \; (n \geqslant 2)\), an integrand \(f(t,p) \, (t \in [0, \infty),\; p \in \mathbb{R}^n)\) -- a function that is \(B\)-measurable with respect to a variable \(t\) and is convex and even in the variable \(p\), \(\nabla u(x)\) -- a gradient (in the sense of Sobolev) of the function \(u \colon \Omega \rightarrow \mathbb{R}\). In the first and the second sections we utilize properties of permutations of differentiable functions and an isoperimetric inequality \(H^{n-1}( \partial A) \geqslant \lambda(m_n A)\), that connects \((n-1)\)-dimensional Hausdorff measure \(H^{n-1}(\partial A )\) of relative boundary \(\partial A\) of the set \(A \subset \Omega\) with its \(n\)-dimensional Lebesgue measure \(m_n A\). The integrand \(f\) is assumed to be isotropic, i.e. \(f(t,p) = f(t,q)\) if \(|p| = |q|\).Applications of the established results to multidimensional variational problems are outlined. For functions \( u \) that vanish on the boundary of the domain \(\Omega\), the assumption of the isotropy of the integrand \( f \) can be omitted. In this case, an important role is played by the Steiner and Schwartz symmetrization operations of the integrand \( f \) and of the function \( u \). The corresponding variants of the lower estimates are discussed in the third section. What is fundamentally new here is that the symmetrization operation is applied not only to the function \(u\), but also to the integrand \(f\). The geometric basis of the results of the third section is the Brunn-Minkowski inequality, as well as the symmetrization properties of the algebraic sum of sets.
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41

Mossino, J., and M. Ughi. "Isoperimetric inequalities and regularity at shrinking points for parabolic problems." Nonlinear Analysis: Theory, Methods & Applications 39, no. 4 (February 2000): 499–517. http://dx.doi.org/10.1016/s0362-546x(98)00217-x.

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42

Almeida, Ricardo, Rui A. C. Ferreira, and Delfim F. M. Torres. "Isoperimetric problems of the calculus of variations with fractional derivatives." Acta Mathematica Scientia 32, no. 2 (March 2012): 619–30. http://dx.doi.org/10.1016/s0252-9602(12)60043-5.

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43

Ghaderi, Sara. "Homotopy Perturbation Method for Solving Moving Boundary and Isoperimetric Problems." Applied Mathematics 03, no. 05 (2012): 403–9. http://dx.doi.org/10.4236/am.2012.35062.

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44

Böröczky, Károly, and Károly Böröczky. "Isoperimetric problems for polytopes with a given number of vertices." Mathematika 43, no. 2 (December 1996): 237–54. http://dx.doi.org/10.1112/s0025579300011748.

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45

Shparlinski, Igor. "Book Review: Report on global methods for combinatorial isoperimetric problems." Mathematics of Computation 74, no. 250 (May 1, 2005): 1033–52. http://dx.doi.org/10.1090/s0025-5718-04-01757-0.

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46

Bentkus, V., and A. Dubickas. "Some isoperimetric inequalities and their application to problems on polynomials." Analysis Mathematica 29, no. 4 (2003): 259–79. http://dx.doi.org/10.1023/b:anam.0000005369.36336.8e.

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47

Exner, Pavel, Evans M. Harrell, and Michael Loss. "Inequalities for Means of Chords, with Application to Isoperimetric Problems." Letters in Mathematical Physics 75, no. 3 (February 22, 2006): 225–33. http://dx.doi.org/10.1007/s11005-006-0053-y.

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48

Martínez, A., and F. Milán. "Affine isoperimetric problems and surfaces with constant affine mean curvature." Manuscripta Mathematica 75, no. 1 (December 1992): 35–41. http://dx.doi.org/10.1007/bf02567069.

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49

Fraser, Craig G. "Isoperimetric problems in the variational calculus of Euler and Lagrange." Historia Mathematica 19, no. 1 (February 1992): 4–23. http://dx.doi.org/10.1016/0315-0860(92)90052-d.

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50

Bénéteau, Catherine, and Dmitry Khavinson. "The Isoperimetric Inequality via Approximation Theory and Free Boundary Problems." Computational Methods and Function Theory 6, no. 2 (December 2006): 253–74. http://dx.doi.org/10.1007/bf03321614.

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