Energy solutions of singular SPDEs on Hilbert spaces with applications to domains with boundary conditions.

Authors

Lukas Gräfner, Nicolas Perkowski, Shyam Popat

Published in

Stochastic partial differential equations : analysis and computations. Volume 14. Issue 2. Pages 1015-1061. Epub Apr 04, 2026.

Abstract

In this paper we extend the theory of energy solutions for singular SPDEs, focusing on equations driven by highly irregular noise with bilinear nonlinearities, including scaling critical examples. By introducing Gelfand triples and leveraging infinite-dimensional analysis in Hilbert spaces together with an integration by parts formula under the invariant measure, we largely eliminate the need for Fourier series and chaos expansions. This approach broadens the applicability of energy solutions to a wider class of SPDEs, offering a unified treatment of various domains and boundary conditions. Our examples are motivated by recent work on scaling limits of interacting particle systems.

PMID:
42405359
Bibliographic data and abstract were imported from PubMed on 06 Jul 2026.

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