Regularity results for discontinuous Hamilton-Jacobi equation with a moving in time boundary
Résumé
In this paper, we present regularizing effect for continuous and bounded by below viscosity solution u of a Hamitlon-Jacobi equation on a moving in time domain. The boundary is described by a time-dependent function b. For each time t > 0, we consider two different Hamiltonians before and after the junction point b(t) and a flux limited condition at b(t). Our regularizing effect result is established by showing that the solution u satisfies in the viscosity sense ut + b ′ (t)ux ≥-η(t) where η is a locally bounded function. As a consequence, we conclude that u is locally Lipschitz continuous.
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