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arXiv · 2006.00779

Convergence of solutions for some degenerate discounted Hamilton--Jacobi equations

Maxime Zavidovique
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Abstract

We study solutions of Hamilton--Jacobi equations of the form $$λα(x) u_λ(x) + H(x, D_x u_λ) = c,$$ where $α$ is a nonnegative function, $λ$ a positive constant, $c$ a constant and $H $ a convex coercive Hamiltonian. Under suitable conditions on $α$ we prove that the functions $u_λ$ converge as $λ\to 0$ to a function $u_0$ that is a solution of the critical equation $H(x, D_x u_0) = c$.

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BibTeXRIS

Maxime Zavidovique. 2021-01-22. Convergence of solutions for some degenerate discounted Hamilton--Jacobi equations. https://doi.org/10.2140/apde.2022.15.1287

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