Gradient Hölder regularity for parabolic normalized \(p(x,t)\)-Laplace equation. (English) Zbl 1470.35093
Summary: We consider the interior Hölder regularity of spatial gradient of viscosity solution to the parabolic normalized \(p(x, t)\)-Laplace equation
\[
u_t = \left( \delta_{i j} + ( p ( x , t ) - 2 ) \frac{ u_i u_j}{ | D u |^2} \right) u_{i j}
\]
with some suitable assumptions on \(p(x, t)\), which arises naturally from a two-player zero-sum stochastic differential game with probabilities depending on space and time.
MSC:
| 35B65 | Smoothness and regularity of solutions to PDEs |
| 35B45 | A priori estimates in context of PDEs |
| 35K92 | Quasilinear parabolic equations with \(p\)-Laplacian |
| 35D40 | Viscosity solutions to PDEs |
Keywords:
parabolic normalized \(p(x, t)\)-Laplacian; stochastic differential game; viscosity solutionReferences:
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