Pathwise uniqueness for stochastic reaction-diffusion equations in Banach spaces with an H\"{o}lder drift component

TL;DR

This paper establishes pathwise uniqueness for a class of stochastic reaction-diffusion equations in Banach spaces with Hölder continuous drift, leveraging space-time white noise and analyzing the Kolmogorov equation.

Contribution

It extends pathwise uniqueness results to Banach space settings with Hölder drift, including models not covered by prior Hilbert space-based work.

Findings

Proves pathwise uniqueness for stochastic reaction-diffusion equations in Banach spaces.

Handles models with Hölder continuous drift terms.

Uses analysis of the Kolmogorov equation to establish results.

Abstract

We prove pathwise uniqueness for an abstract stochastic reaction-diffusion equation in Banach spaces. The drift contains a bounded H\"{o}lder term; in spite of this, due to the space-time white noise it is possible to prove pathwise uniqueness. The proof is based on a detailed analysis of the associated Kolmogorov equation. The model includes examples not covered by the previous works based on Hilbert spaces or concrete SPDEs.