Well-posedness of stochastic evolution equations with H\"older
continuous noise
Well-posedness of stochastic evolution equations with H\"older
continuous noise
We show existence and pathwise uniqueness of probabilistically strong solutions to a pseudomonotone stochastic evolution problem on a bounded domain $D\subseteq\mathbb{R}^d$, $d\in\mathbb{N}$, with homogeneous Dirichlet boundary conditions and random initial data $u_0\in L^2(\Omega;L^2(D))$. The main novelty is the presence of a merely H\"older continuous multiplicative noise term. In order to …