Energy solutions of singular SPDEs on Hilbert spaces with applications to domains with boundary conditions
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.
Fields of Study & Subjects
Advanced Mathematical Modeling in Engineering
Contact Mechanics and Variational Inequalities
Stability and Controllability of Differential Equations
Publication details
- Journal / source
- Stochastic Partial Differential Equations Analysis and Computations
- Publisher
- Springer Science and Business Media LLC
- Volume
- 14
- Issue
- 2
- Pages
- 1015–1061
- Publication date
- 4 April 2026
- Language
- EN