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  1. Nonlinear Differential Equations and Applications NoDEA
  2. Nonlinear Differential Equations and Applications NoDEA : Volume 21
  3. Nonlinear Differential Equations and Applications NoDEA : Volume 21, Issue 2, April 2014
  4. The Mather problem for lower semicontinuous Lagrangians
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Nonlinear Differential Equations and Applications NoDEA : Volume 23
Nonlinear Differential Equations and Applications NoDEA : Volume 22
Nonlinear Differential Equations and Applications NoDEA : Volume 21
Nonlinear Differential Equations and Applications NoDEA : Volume 21, Issue 6, December 2014
Nonlinear Differential Equations and Applications NoDEA : Volume 21, Issue 5, October 2014
Nonlinear Differential Equations and Applications NoDEA : Volume 21, Issue 4, August 2014
Nonlinear Differential Equations and Applications NoDEA : Volume 21, Issue 3, June 2014
Nonlinear Differential Equations and Applications NoDEA : Volume 21, Issue 2, April 2014
An elementary approach to the inviscid limits for the 3D Navier–Stokes equations with slip boundary conditions and applications to the 3D Boussinesq equations
The Mather problem for lower semicontinuous Lagrangians
An approximation scheme for the anisotropic and nonlocal mean curvature flow
An Osgood type regularity criterion for the liquid crystal flows
Wellposedness in the Lipschitz class for a quasi-linear hyperbolic system arising from a model of the atmosphere including water phase transitions
Numerical extremal solutions for a mixed problem with singular $${\phi}$$ ϕ -Laplacian
Nonlinear Differential Equations and Applications NoDEA : Volume 21, Issue 1, February 2014
Nonlinear Differential Equations and Applications NoDEA : Volume 20
Nonlinear Differential Equations and Applications NoDEA : Volume 19
Nonlinear Differential Equations and Applications NoDEA : Volume 18
Nonlinear Differential Equations and Applications NoDEA : Volume 17
Nonlinear Differential Equations and Applications NoDEA : Volume 16
Nonlinear Differential Equations and Applications NoDEA : Volume 15
Nonlinear Differential Equations and Applications NoDEA : Volume 14
Nonlinear Differential Equations and Applications NoDEA : Volume 13
Nonlinear Differential Equations and Applications NoDEA : Volume 12
Nonlinear Differential Equations and Applications NoDEA : Volume 11
Nonlinear Differential Equations and Applications NoDEA : Volume 10
Nonlinear Differential Equations and Applications NoDEA : Volume 9
Nonlinear Differential Equations and Applications NoDEA : Volume 8
Nonlinear Differential Equations and Applications NoDEA : Volume 7
Nonlinear Differential Equations and Applications NoDEA : Volume 6
Nonlinear Differential Equations and Applications NoDEA : Volume 5
Nonlinear Differential Equations and Applications NoDEA : Volume 4

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The Mather problem for lower semicontinuous Lagrangians

Content Provider SpringerLink
Author Gomes, Diogo A. Terrone, Gabriele
Copyright Year 2013
Abstract In this paper we develop the Aubry-Mather theory for Lagrangians in which the potential energy can be discontinuous. Namely we assume that the Lagrangian is lower semicontinuous in the state variable, piecewise smooth with a (smooth) discontinuity surface, as well as coercive and convex in the velocity. We establish existence of Mather measures, various approximation results, partial regularity of viscosity solutions away from the singularity, invariance by the Euler–Lagrange flow away from the singular set, and further jump conditions that correspond to conservation of energy and tangential momentum across the discontinuity.
Ending Page 217
Page Count 51
Starting Page 167
File Format PDF
ISSN 10219722
e-ISSN 14209004
Journal Nonlinear Differential Equations and Applications NoDEA
Issue Number 2
Volume Number 21
Language English
Publisher Springer Basel
Publisher Date 2013-08-01
Publisher Place Basel
Access Restriction One Nation One Subscription (ONOS)
Subject Keyword Hamilton-Jacobi equations Partial differential equations with discontinuous coefficients or data Action minimizing measures Analysis Discontinuous Lagrangians Action-minimizing orbits and measures Hamilton–Jacobi equations Problems involving partial differential equations Viscosity solutions
Content Type Text
Resource Type Article
Subject Applied Mathematics Analysis
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