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Mathematics > Probability
Title: Weak uniqueness by noise for singular stochastic PDEs
(Submitted on 3 Aug 2023 (v1), last revised 27 Mar 2024 (this version, v2))
Abstract: We prove weak uniqueness of mild solutions for a general class of SPDEs on a Hilbert space. The main novelty is that the drift is only defined on a Sobolev-type subspace and no H\"older-continuity assumptions are required. This allows us to cover examples such as equations with divergence-form and non-divergence-form drift, and Cahn--Hilliard-type equations with possibly singular perturbations. The main idea is to consider a suitable coloured Wiener noise so that both the solvability of the SPDE and the regularising effect of the Kolmogorov operator are preserved via stochastic maximal regularity results. As a by-product, this also allows us to generalise the available results of uniqueness by noise for perturbations of the heat equation to higher dimensions.
Submission history
From: Luca Scarpa [view email][v1] Thu, 3 Aug 2023 09:19:00 GMT (35kb)
[v2] Wed, 27 Mar 2024 11:30:52 GMT (38kb)
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