The existence and uniqueness result for Quasilinear Stochastic PDEs with Obstacle under weaker integrability conditions

TL;DR

This paper establishes an existence and uniqueness theorem for quasilinear stochastic partial differential equations with obstacles, under less restrictive integrability conditions on the coefficients and barriers, advancing the mathematical theory of such equations.

Contribution

It introduces weaker integrability conditions for the coefficients and barriers in quasilinear stochastic PDEs with obstacles, broadening the applicability of existence and uniqueness results.

Findings

Proved existence of solutions under weaker conditions

Established uniqueness of solutions in the new setting

Extended theoretical framework for OSPDEs

Abstract

We prove an existence and uniqueness result for quasilinear Stochastic PDEs with Obstacle (in short OSPDE) under a weaker integrability condition on the coefficient and the barrier.