Mild solutions to semilinear stochastic partial differential equations with locally monotone coefficients

TL;DR

This paper establishes existence and uniqueness of mild solutions for semilinear stochastic PDEs with locally monotone coefficients using a semigroup approach and dilation theorem, also discussing solution properties like the Markov property.

Contribution

It introduces a novel approach combining the semigroup method with Nagy's dilation theorem to handle locally monotone coefficients in stochastic PDEs.

Findings

Proved existence and uniqueness of mild solutions.

Applied dilation theorem to reduce problem complexity.

Discussed properties such as the Markov property.

Abstract

We provide an existence and uniqueness result for mild solutions to semilinear stochastic partial differential equations in the framework of the semigroup approach with locally monotone coefficients. An important component of the proof is an application of the dilation theorem of Nagy, which allows us to reduce the problem to infinite dimensional stochastic differential equations on a larger Hilbert space. Properties of the solutions like the Markov property are discussed as well.