Level sets of solutions to the stationary Hamilton-Jacobi equation are John regular

2023/12/29 by Davoli, Elisa, Stefanelli, Ulisse · 1 citation
#35B65 #35F21 #Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.2312.17635

Abstract

Let u be the unique nonnegative viscosity solution of the Hamilton-Jacobi equation H(x,∇ u)=0 in the external domain \mathbb R ⁿ ∖ K with u=0 on K. Under general conditions on H, we prove that all sublevels of u are John domains. Moreover, if K itself is a John domain, we provide a uniform lower bound on the John constant of all sublevels. We exhibit counterexamples showing that John regularity is sharp in this setting.

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