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  1. Calculus of Variations and Partial Differential Equations
  2. Calculus of Variations and Partial Differential Equations : Volume 35
  3. Calculus of Variations and Partial Differential Equations : Volume 35, Issue 4, August 2009
  4. Further PDE methods for weak KAM theory
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Calculus of Variations and Partial Differential Equations : Volume 56
Calculus of Variations and Partial Differential Equations : Volume 55
Calculus of Variations and Partial Differential Equations : Volume 54
Calculus of Variations and Partial Differential Equations : Volume 53
Calculus of Variations and Partial Differential Equations : Volume 52
Calculus of Variations and Partial Differential Equations : Volume 51
Calculus of Variations and Partial Differential Equations : Volume 50
Calculus of Variations and Partial Differential Equations : Volume 49
Calculus of Variations and Partial Differential Equations : Volume 48
Calculus of Variations and Partial Differential Equations : Volume 47
Calculus of Variations and Partial Differential Equations : Volume 46
Calculus of Variations and Partial Differential Equations : Volume 45
Calculus of Variations and Partial Differential Equations : Volume 44
Calculus of Variations and Partial Differential Equations : Volume 43
Calculus of Variations and Partial Differential Equations : Volume 42
Calculus of Variations and Partial Differential Equations : Volume 41
Calculus of Variations and Partial Differential Equations : Volume 40
Calculus of Variations and Partial Differential Equations : Volume 39
Calculus of Variations and Partial Differential Equations : Volume 38
Calculus of Variations and Partial Differential Equations : Volume 37
Calculus of Variations and Partial Differential Equations : Volume 36
Calculus of Variations and Partial Differential Equations : Volume 35
Calculus of Variations and Partial Differential Equations : Volume 35, Issue 4, August 2009
A structure theorem of Dirac-harmonic maps between spheres
A two-phase obstacle-type problem for the p-Laplacian
Further PDE methods for weak KAM theory
Solutions of elliptic problems with nonlinearities of linear growth
Necessity of a Wiener type condition for boundary regularity of quasiminimizers and nonlinear elliptic equations
On critical normal sections for two-dimensional immersions in $${\mathbb R^{n+2}}$$
Intrinsic regular submanifolds in Heisenberg groups are differentiable graphs
C 1 regularity of solutions of the Monge–Ampère equation for optimal transport in dimension two
Calculus of Variations and Partial Differential Equations : Volume 35, Issue 3, July 2009
Calculus of Variations and Partial Differential Equations : Volume 35, Issue 2, June 2009
Calculus of Variations and Partial Differential Equations : Volume 35, Issue 1, May 2009
Calculus of Variations and Partial Differential Equations : Volume 34
Calculus of Variations and Partial Differential Equations : Volume 33
Calculus of Variations and Partial Differential Equations : Volume 32
Calculus of Variations and Partial Differential Equations : Volume 31
Calculus of Variations and Partial Differential Equations : Volume 30
Calculus of Variations and Partial Differential Equations : Volume 29
Calculus of Variations and Partial Differential Equations : Volume 28
Calculus of Variations and Partial Differential Equations : Volume 27
Calculus of Variations and Partial Differential Equations : Volume 26
Calculus of Variations and Partial Differential Equations : Volume 25
Calculus of Variations and Partial Differential Equations : Volume 24
Calculus of Variations and Partial Differential Equations : Volume 23
Calculus of Variations and Partial Differential Equations : Volume 22
Calculus of Variations and Partial Differential Equations : Volume 21
Calculus of Variations and Partial Differential Equations : Volume 20
Calculus of Variations and Partial Differential Equations : Volume 19
Calculus of Variations and Partial Differential Equations : Volume 18
Calculus of Variations and Partial Differential Equations : Volume 17
Calculus of Variations and Partial Differential Equations : Volume 16
Calculus of Variations and Partial Differential Equations : Volume 15
Calculus of Variations and Partial Differential Equations : Volume 14
Calculus of Variations and Partial Differential Equations : Volume 13
Calculus of Variations and Partial Differential Equations : Volume 12
Calculus of Variations and Partial Differential Equations : Volume 11
Calculus of Variations and Partial Differential Equations : Volume 10
Calculus of Variations and Partial Differential Equations : Volume 9
Calculus of Variations and Partial Differential Equations : Volume 8
Calculus of Variations and Partial Differential Equations : Volume 7
Calculus of Variations and Partial Differential Equations : Volume 6
Calculus of Variations and Partial Differential Equations : Volume 5

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Further PDE methods for weak KAM theory

Content Provider SpringerLink
Author Evans, Lawrence C.
Copyright Year 2008
Abstract We introduce and make estimates for several new approximations that in appropriate asymptotic limits yield the key PDE for weak KAM theory, namely a Hamilton–Jacobi type equation for a potential u and a coupled transport equation for a measure σ. We revisit as well a singular variational approximation introduced in Evans (Calc Vari Partial Differ Equ 17:159–177, 2003) and demonstrate “approximate integrability” of certain phase space dynamics related to the Hamiltonian flow. Other examples include a pair of strongly coupled PDE suggested by the Lions–Lasry theory (Lasry and Lions in Japan J Math 2:229–260, 2007) of mean field games and a new and extremely singular elliptic equation suggested by sup-norm variational theory.
Ending Page 462
Page Count 28
Starting Page 435
File Format PDF
ISSN 09442669
e-ISSN 14320835
Journal Calculus of Variations and Partial Differential Equations
Issue Number 4
Volume Number 35
Language English
Publisher Springer-Verlag
Publisher Date 2008-11-18
Publisher Place Berlin, Heidelberg
Access Restriction One Nation One Subscription (ONOS)
Subject Keyword Calculus of Variations and Optimal Control; Optimization Systems Theory, Control Mathematical and Computational Physics Analysis Variational methods for second-order elliptic equations Action-minimizing orbits and measures Nonlinear first-order equations
Content Type Text
Resource Type Article
Subject Applied Mathematics Analysis
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