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Title of Journal: Calc Var

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Abbravation: Calculus of Variations and Partial Differential Equations

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Springer Berlin Heidelberg

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DOI

10.1007/s12250-008-2979-y

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1432-0835

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Weak KAM theory for a weakly coupled system of Ham

Authors: Alessio Figalli Diogo Gomes Diego Marcon
Publish Date: 2016/06/22
Volume: 55, Issue: 4, Pages: 79-
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Abstract

Here we extend the weak KAM and Aubry–Mather theories to optimal switching problems We consider three issues the analysis of the calculus of variations problem the study of a generalized weak KAM theorem for solutions of weakly coupled systems of Hamilton–Jacobi equations and the longtime behavior of timedependent systems We prove the existence and regularity of action minimizers obtain necessary conditions for minimality extend Fathi’s weak KAM theorem and describe the asymptotic limit of the generalized Lax–Oleinik semigroupA Figalli is partially supported by the NSF Grants DMS1262411 and DMS1361122 D Gomes was partially supported by KAUST baseline and startup funds D Marcon was partially supported by the UT AustinPortugal partnership through the FCT doctoral fellowship SFRH/BD/33919/2009

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  1. Asymptotic behavior at isolated singularities for solutions of nonlocal semilinear elliptic systems of inequalities
  2. Fractional Poincaré inequality with finite total Q -curvature
  3. Solitary waves for a class of quasilinear Schrödinger equations in dimension two
  4. Thick clusters for the radially symmetric nonlinear Schrödinger equation
  5. On elliptic systems with Sobolev critical growth
  6. Critical points for functionals with quasilinear singular Euler–Lagrange equations
  7. Duality for rectified cost functions
  8. An approach to minimization under a constraint: the added mass technique
  9. Single-point condensation phenomena for a four-dimensional biharmonic Ren–Wei problem
  10. Uniqueness and nondegeneracy of positive radial solutions of $$\mathbf {div\,{\varvec{(}}{\varvec{\rho }} \nabla u{\varvec{)}} +{\varvec{\rho }}{\varvec{(}}-gu+hu^p{\varvec{)}}=0}$$
  11. Second order estimates for Hessian type fully nonlinear elliptic equations on Riemannian manifolds
  12. Lower bounds of Dirichlet eigenvalues for some degenerate elliptic operators
  13. Sharp energy estimates for nonlinear fractional diffusion equations
  14. On Newton equations which are totally integrable at infinity
  15. Energy asymptotics for Type II superconductors
  16. Regularity for fully nonlinear nonlocal parabolic equations with rough kernels
  17. Singular points of Hölder asymptotically optimally doubling measures
  18. Cahn–Hilliard–Navier–Stokes systems with moving contact lines
  19. A mean field type flow part I: compactness of solutions to a perturbed mean field type equation
  20. Boundary value problems for Willmore curves in $$\mathbb {R}^2$$
  21. Fractional eigenvalues
  22. On a quasilinear system involving the operator curl
  23. A Penrose inequality for graphs over Kottler space
  24. Moser–Trudinger inequalities of vector bundle over a compact Riemannian manifold of dimension 2
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