The Obstacle Problem for Quasilinear Stochastic PDEs with Degenerate Operator

TL;DR

This paper establishes the existence and uniqueness of solutions for degenerate quasilinear stochastic PDEs with obstacles, utilizing De Giorgi's iteration to derive $L^p$ estimates for weak solutions.

Contribution

It introduces a novel approach to handle degenerate OSPDEs, proving existence, uniqueness, and regularity estimates in this challenging setting.

Findings

Proved existence and uniqueness of solutions.

Derived $L^p$ estimates for weak solutions.

Applied De Giorgi's iteration to degenerate stochastic PDEs.

Abstract

We prove the existence and uniqueness of solution of quasilinear stochastic partial differential equations with obstacle (OSPDEs in short) in degenerate case. Using De Giorgi's iteration, we deduce the $L^p-$estimates for the time-space uniform norm of weak solutions.