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

TL;DR

This paper extends previous work on semilinear stochastic partial differential equations by establishing existence and uniqueness of mild solutions with more general conditions, including pseudo-contractive semigroups and Poisson measures.

Contribution

It provides a broader existence and uniqueness result for mild solutions, incorporating Poisson random measures and pseudo-contractive semigroups, improving earlier contraction-only frameworks.

Findings

Established existence and uniqueness of solutions under new conditions

Extended the framework to include Poisson random measures

Allowed for pseudo-contractive semigroups in the analysis

Abstract

In this addendum we provide an existence and uniqueness result for mild solutions to semilinear stochastic partial differential equations driven by Wiener processes and Poisson random measures in the framework of the semigroup approach with locally monotone coefficients, where the semigroup is allowed to be pseudo-contractive. This improves an earlier paper of the author, where the equation was only driven by Wiener processes, and where the semigroup was only allowed to be a semigroup of contractions.