Selection problems for a discount degenerate viscous Hamilton-Jacobi equation

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• 作者：Hiroyoshi Mitake^a ; ^{hiroyoshi-mitake@hiroshima-u.ac.jp} ; Hung V. Tran^b ; ^{hung@math.wisc.edu}
• 关键词：35B40 ; 37J50 ; 49L25
• 刊名：Advances in Mathematics
• 出版年：2017
• 出版时间：14 January 2017
• 年：2017
• 卷：306
• 期：Complete
• 页码：684-703
• 全文大小：400 K
• 卷排序：306

文摘

We prove that the solution of the discounted approximation of a degenerate viscous Hamilton–Jacobi equation with convex Hamiltonians converges to that of the associated ergodic problem. We characterize the limit in terms of stochastic Mather measures by using the nonlinear adjoint method and deriving a commutation lemma. This convergence result was first proven by Davini, Fathi, Iturriaga, and Zavidovique for first order Hamilton–Jacobi equations.