Coercivity condition for higher order moments for nonlinear SPDEs and existence of solution under local monotonicity

TL;DR

This paper establishes coercivity conditions for higher order moments in nonlinear SPDEs and extends existence and uniqueness results to include derivatives in the operators under local monotonicity.

Contribution

It introduces coercivity conditions for higher moments and broadens existence results to operators with derivatives in the stochastic integral for nonlinear SPDEs.

Findings

Higher order moment estimates under coercivity conditions

Extended existence and uniqueness results for nonlinear SPDEs

Operators with derivatives in the stochastic integral are accommodated

Abstract

Higher order moment estimates for solutions to nonlinear SPDEs governed by locally-monotone operators are obtained under appropriate coercivity condition. These are then used to extend known existence and uniqueness results for nonlinear SPDEs under local monotonicity conditions to allow derivatives in the operator acting on the solution under the stochastic integral.