Abstract
In this paper, we present the regularizing effects for a continuous and bounded viscosity solution u of a Hamilton-Jacobi equation on a time-dependent domain. The boundary is defined by a time-dependent function b ( t ) . For each time t>0, we consider two distinct Hamiltonians before and after the junction point b ( t ) , along with a flux-limited condition at b ( t ) . Our result on the regularizing effects is established by proving that the solution u satisfies, in the viscosity sense, u t + b ′ ( t ) u x ≥ − η ( t ) , where η is a locally bounded function. Consequently, we conclude that u is locally Lipschitz continuous.
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