-
Previous Article
Spectral theory for nonconservative transmission line networks
- NHM Home
- This Issue
-
Next Article
Convergence of discrete duality finite volume schemes for the cardiac bidomain model
Perturbation and numerical methods for computing the minimal average energy
1. | Department of Mathematics, 1 University Station C1200, Austin, TX 78712-0257, United States |
2. | Department of Mathematics, The University of Texas at Austin, 1 University Station C1200, Austin, TX 78712-0257 |
References:
[1] |
V. Bangert, The existence of gaps in minimal foliations, Aequationes Math., 34 (1987), 153-166.
doi: 10.1007/BF01830667. |
[2] |
V. Bangert, A uniqueness theorem for $Z$n-periodic variational problems, Comment. Math. Helv., 62 (1987), 511-531.
doi: 10.1007/BF02564459. |
[3] |
V. Bangert, On minimal laminations of the torus, Ann. Inst. H. Poincaré Anal. Non Linéaire, 6 (1989), 95-138. |
[4] |
T. Blass, R. de la Llave and E. Valdinoci, A comparison principle for a Sobolev gradient semi-flow, Commun. Pure Appl. Anal., 10 (2011), 69-91. |
[5] |
L. Chierchia and C. Falcolini, A note on quasi-periodic solutions of some elliptic systems, Z. Angew. Math. Phys., 47 (1996), 210-220.
doi: 10.1007/BF00916825. |
[6] |
L. C. Evans, "Partial Differential Equations," volume 19 of "Graduate Studies in Mathematics," American Mathematical Society, Providence, RI, 1998. |
[7] |
T. Kato, "Perturbation Theory for Linear Operators," Die Grundlehren der mathematischen Wissenschaften, Band 132. Springer-Verlag New York, Inc., New York, 1966. |
[8] |
R. de la Llave and E. Valdinoci, A generalization of Aubry-Mather theory to partial differential equations and pseudo-differential equations, Ann. Inst. H. Poincaré Anal. Non Linéaire, 26 (2009), 1309-1344. |
[9] |
M. Morse, "Variational Analysis: Critical Extremals and Sturmian Extensions," Interscience Publishers [John Wiley & Sons, Inc.], New York-London-Sydney, 1973. |
[10] |
J. Moser, Minimal solutions of variational problems on a torus, Ann. Inst. H. Poincaré Anal. Non Linéaire, 3 (1986), 229-272. |
[11] |
J. W. Neuberger, "Sobolev Gradients and Differential Equations," volume 1670 of "Lecture Notes in Mathematics," Springer-Verlag, Berlin, second edition, 2010. |
[12] |
L. Nirenberg, On elliptic partial differential equations, Ann. Scuola Norm. Sup. Pisa(3), 13 (1959), 115-162. |
[13] |
W. Senn, Strikte Konvexität fär Variationsprobleme auf dem $n$-dimensionalen Torus, Manuscripta Math., 71 (1991), 45-65.
doi: 10.1007/BF02568393. |
[14] |
W. M. Senn, Differentiability properties of the minimal average action, Calc. Var. Partial Differential Equations, 3 (1995), 343-384. |
show all references
References:
[1] |
V. Bangert, The existence of gaps in minimal foliations, Aequationes Math., 34 (1987), 153-166.
doi: 10.1007/BF01830667. |
[2] |
V. Bangert, A uniqueness theorem for $Z$n-periodic variational problems, Comment. Math. Helv., 62 (1987), 511-531.
doi: 10.1007/BF02564459. |
[3] |
V. Bangert, On minimal laminations of the torus, Ann. Inst. H. Poincaré Anal. Non Linéaire, 6 (1989), 95-138. |
[4] |
T. Blass, R. de la Llave and E. Valdinoci, A comparison principle for a Sobolev gradient semi-flow, Commun. Pure Appl. Anal., 10 (2011), 69-91. |
[5] |
L. Chierchia and C. Falcolini, A note on quasi-periodic solutions of some elliptic systems, Z. Angew. Math. Phys., 47 (1996), 210-220.
doi: 10.1007/BF00916825. |
[6] |
L. C. Evans, "Partial Differential Equations," volume 19 of "Graduate Studies in Mathematics," American Mathematical Society, Providence, RI, 1998. |
[7] |
T. Kato, "Perturbation Theory for Linear Operators," Die Grundlehren der mathematischen Wissenschaften, Band 132. Springer-Verlag New York, Inc., New York, 1966. |
[8] |
R. de la Llave and E. Valdinoci, A generalization of Aubry-Mather theory to partial differential equations and pseudo-differential equations, Ann. Inst. H. Poincaré Anal. Non Linéaire, 26 (2009), 1309-1344. |
[9] |
M. Morse, "Variational Analysis: Critical Extremals and Sturmian Extensions," Interscience Publishers [John Wiley & Sons, Inc.], New York-London-Sydney, 1973. |
[10] |
J. Moser, Minimal solutions of variational problems on a torus, Ann. Inst. H. Poincaré Anal. Non Linéaire, 3 (1986), 229-272. |
[11] |
J. W. Neuberger, "Sobolev Gradients and Differential Equations," volume 1670 of "Lecture Notes in Mathematics," Springer-Verlag, Berlin, second edition, 2010. |
[12] |
L. Nirenberg, On elliptic partial differential equations, Ann. Scuola Norm. Sup. Pisa(3), 13 (1959), 115-162. |
[13] |
W. Senn, Strikte Konvexität fär Variationsprobleme auf dem $n$-dimensionalen Torus, Manuscripta Math., 71 (1991), 45-65.
doi: 10.1007/BF02568393. |
[14] |
W. M. Senn, Differentiability properties of the minimal average action, Calc. Var. Partial Differential Equations, 3 (1995), 343-384. |
[1] |
Antonin Chambolle, Gilles Thouroude. Homogenization of interfacial energies and construction of plane-like minimizers in periodic media through a cell problem. Networks and Heterogeneous Media, 2009, 4 (1) : 127-152. doi: 10.3934/nhm.2009.4.127 |
[2] |
V. Mastropietro, Michela Procesi. Lindstedt series for periodic solutions of beam equations with quadratic and velocity dependent nonlinearities. Communications on Pure and Applied Analysis, 2006, 5 (1) : 1-28. doi: 10.3934/cpaa.2006.5.1 |
[3] |
Tien-Tsan Shieh. From gradient theory of phase transition to a generalized minimal interface problem with a contact energy. Discrete and Continuous Dynamical Systems, 2016, 36 (5) : 2729-2755. doi: 10.3934/dcds.2016.36.2729 |
[4] |
G. Gentile, V. Mastropietro. Convergence of Lindstedt series for the non linear wave equation. Communications on Pure and Applied Analysis, 2004, 3 (3) : 509-514. doi: 10.3934/cpaa.2004.3.509 |
[5] |
Michele V. Bartuccelli, G. Gentile, Kyriakos V. Georgiou. Kam theory, Lindstedt series and the stability of the upside-down pendulum. Discrete and Continuous Dynamical Systems, 2003, 9 (2) : 413-426. doi: 10.3934/dcds.2003.9.413 |
[6] |
Robert Jensen, Andrzej Świech. Uniqueness and existence of maximal and minimal solutions of fully nonlinear elliptic PDE. Communications on Pure and Applied Analysis, 2005, 4 (1) : 199-207. doi: 10.3934/cpaa.2005.4.187 |
[7] |
Peter Takáč. Stabilization of positive solutions for analytic gradient-like systems. Discrete and Continuous Dynamical Systems, 2000, 6 (4) : 947-973. doi: 10.3934/dcds.2000.6.947 |
[8] |
Herbert Gajewski, Jens A. Griepentrog. A descent method for the free energy of multicomponent systems. Discrete and Continuous Dynamical Systems, 2006, 15 (2) : 505-528. doi: 10.3934/dcds.2006.15.505 |
[9] |
Elena Nozdrinova, Olga Pochinka. Solution of the 33rd Palis-Pugh problem for gradient-like diffeomorphisms of a two-dimensional sphere. Discrete and Continuous Dynamical Systems, 2021, 41 (3) : 1101-1131. doi: 10.3934/dcds.2020311 |
[10] |
Martí Prats. Beltrami equations in the plane and Sobolev regularity. Communications on Pure and Applied Analysis, 2018, 17 (2) : 319-332. doi: 10.3934/cpaa.2018018 |
[11] |
Diego Castellaneta, Alberto Farina, Enrico Valdinoci. A pointwise gradient estimate for solutions of singular and degenerate pde's in possibly unbounded domains with nonnegative mean curvature. Communications on Pure and Applied Analysis, 2012, 11 (5) : 1983-2003. doi: 10.3934/cpaa.2012.11.1983 |
[12] |
Alessio Figalli, Vito Mandorino. Fine properties of minimizers of mechanical Lagrangians with Sobolev potentials. Discrete and Continuous Dynamical Systems, 2011, 31 (4) : 1325-1346. doi: 10.3934/dcds.2011.31.1325 |
[13] |
Federica Mennuni, Addolorata Salvatore. Existence of minimizers for a quasilinear elliptic system of gradient type. Discrete and Continuous Dynamical Systems - S, 2022 doi: 10.3934/dcdss.2022013 |
[14] |
Maurizio Grasselli, Morgan Pierre. Convergence to equilibrium of solutions of the backward Euler scheme for asymptotically autonomous second-order gradient-like systems. Communications on Pure and Applied Analysis, 2012, 11 (6) : 2393-2416. doi: 10.3934/cpaa.2012.11.2393 |
[15] |
Armands Gritsans, Felix Sadyrbaev. The Nehari solutions and asymmetric minimizers. Conference Publications, 2015, 2015 (special) : 562-568. doi: 10.3934/proc.2015.0562 |
[16] |
Dominique Lecomte. Hurewicz-like tests for Borel subsets of the plane. Electronic Research Announcements, 2005, 11: 95-102. |
[17] |
Annalisa Cesaroni, Matteo Novaga. Volume constrained minimizers of the fractional perimeter with a potential energy. Discrete and Continuous Dynamical Systems - S, 2017, 10 (4) : 715-727. doi: 10.3934/dcdss.2017036 |
[18] |
Peter A. Hästö. On the existance of minimizers of the variable exponent Dirichlet energy integral. Communications on Pure and Applied Analysis, 2006, 5 (3) : 415-422. doi: 10.3934/cpaa.2006.5.415 |
[19] |
Xiaming Chen. Kernel-based online gradient descent using distributed approach. Mathematical Foundations of Computing, 2019, 2 (1) : 1-9. doi: 10.3934/mfc.2019001 |
[20] |
Ting Hu. Kernel-based maximum correntropy criterion with gradient descent method. Communications on Pure and Applied Analysis, 2020, 19 (8) : 4159-4177. doi: 10.3934/cpaa.2020186 |
2020 Impact Factor: 1.213
Tools
Metrics
Other articles
by authors
[Back to Top]