The vanishing discount problem and viscosity Mather measures. Part 2: boundary value problems
arXiv:1607.04709 · doi:10.1016/j.matpur.2016.11.002
Abstract
In arXiv:1603.01051 (Part 1 of this series), we have introduced a variational approach to studying the vanishing discount problem for fully nonlinear, degenerate elliptic, partial differential equations in a torus. We develop this approach further here to handle boundary value problems. In particular, we establish new representation formulas for solutions of discount problems, critical values, and use them to prove convergence results for the vanishing discount problems.
40 pages
References in corpus (4)
- Convergence of the solutions of the discounted equation
- Convergence of the solutions of the discounted equation: the discrete case
- The vanishing discount problem and viscosity Mather measures. Part 1: the problem on a torus
- Selection problems for a discounted degenerate viscous Hamilton--Jacobi equation
Cited by in corpus (15)
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- State-constraint static Hamilton-Jacobi equations in nested domains
- Convergence of solutions of Hamilton-Jacobi equations depending nonlinearly on the unknown function
- Remarks on the vanishing viscosity process of state-constraint Hamilton-Jacobi equations
- Herglotz' variational principle and Lax-Oleinik evolution
- Limit of solutions for semilinear Hamilton-Jacobi equations with degenerate viscosity
- The selection problem for some first-order stationary mean-field games
- An example in the vanishing discount problem for monotone systems of Hamilton-Jacobi equations
- On the regularity of stochastic effective Hamiltonian
- On the vanishing contact structure for viscosity solutions of contact type Hamilton-Jacobi equations I: Cauchy problem
- Exponential convergence of 1-graph of the solution semigroup of contact Hamilton-Jacobi equations
- Vanishing discount limits for first-order fully nonlinear Hamilton-Jacobi equations on noncompact domains