Marinelli, C;
Scarpa, L;
(2018)
Strong solutions to SPDEs with monotone drift in divergence form.
Stochastics and Partial Differential Equations: Analysis and Computations
, 6
(3)
pp. 364-396.
10.1007/s40072-018-0111-3.
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Abstract
We prove existence and uniqueness of strong solutions, as well as continuous dependence on the initial datum, for a class of fully nonlinear second-order stochastic PDEs with drift in divergence form. Due to rather general assumptions on the growth of the nonlinearity in the drift, which, in particular, is allowed to grow faster than polynomially, existing techniques are not applicable. A well-posedness result is obtained through a combination of a priori estimates on regularized equations, interpreted both as stochastic equations as well as deterministic equations with random coefficients, and weak compactness arguments. The result is essentially sharp, in the sense that no extra hypotheses are needed, bar continuity of the nonlinear function in the drift, with respect to the deterministic theory.
| Type: | Article |
|---|---|
| Title: | Strong solutions to SPDEs with monotone drift in divergence form |
| Open access status: | An open access version is available from UCL Discovery |
| DOI: | 10.1007/s40072-018-0111-3 |
| Publisher version: | https://doi.org/10.1007/s40072-018-0111-3 |
| Language: | English |
| Additional information: | This article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made. |
| Keywords: | Stochastic evolution equations · Singular drift · Divergence form · Multiplicative noise · Monotone operators |
| UCL classification: | UCL UCL > Provost and Vice Provost Offices > UCL BEAMS UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences > Dept of Mathematics |
| URI: | https://discovery.ucl.ac.uk/id/eprint/1546709 |
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