Publications
Stochastic PDEs via convex minimization
- Author(s)
- Luca Scarpa, Ulisse Stefanelli
- Abstract
We prove the applicability of the Weighted Energy-Dissipation (WED) variational principle to nonlinear parabolic stochastic partial differential equations in abstract form. The WED principle consists in the minimization of a parameter-dependent convex functional on entire trajectories. Its unique minimizers correspond to elliptic-in-time regularizations of the stochastic differential problem. As the regularization parameter tends to zero, solutions of the limiting problem are recovered. This in particular provides a direct approach via convex optimization to the approximation of nonlinear stochastic partial differential equations.
- Organisation(s)
- Department of Mathematics, Research Platform Accelerating Photoreaction Discovery
- External organisation(s)
- Institute of Genetics and Biophysics "Adriano Buzzati-Traverso", CNR
- Journal
- Communications in Partial Differential Equations
- Volume
- 46
- Pages
- 66-97
- No. of pages
- 32
- ISSN
- 0360-5302
- DOI
- https://doi.org/10.1080/03605302.2020.1831017
- Publication date
- 2021
- Peer reviewed
- Yes
- Austrian Fields of Science 2012
- 101002 Analysis
- Keywords
- ASJC Scopus subject areas
- Analysis, Applied Mathematics
- Portal url
- https://ucris.univie.ac.at/portal/en/publications/stochastic-pdes-via-convex-minimization(6ec43a9b-66db-4855-a39f-ac4b656a77c8).html