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On the well-posedness of SPDEs with singular drift in divergence form

Marinelli, C; Scarpa, L; (2018) On the well-posedness of SPDEs with singular drift in divergence form. In: Proceedings of the International Conference on Stochastic Partial Differential Equations and Related Fields: SPDERF 2016. (pp. pp. 225-235). Springer, Cham: Bielefeld, Germany. Green open access

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Abstract

We prove existence and uniqueness of strong solutions for a class of second-order stochastic PDEs with multiplicative Wiener noise and drift of the form divγ (∇.), where γ is a maximal monotone graph in ℝn× ℝnobtained as the subdifferential of a convex function satisfying very mild assumptions on its behavior at infinity. The well-posedness result complements the corresponding one in our recent work arXiv:1612.08260 where, under the additional assumption that γ is single-valued, a solution with better integrability and regularity properties is constructed. The proof given here, however, is self-contained.

Type: Proceedings paper
Title: On the well-posedness of SPDEs with singular drift in divergence form
Event: International Conference on Stochastic Partial Differential Equations and Related Fields: SPDERF 2016
Open access status: An open access version is available from UCL Discovery
DOI: 10.1007/978-3-319-74929-7_12
Publisher version: https://doi.org/10.1007/978-3-319-74929-7_12
Language: English
Additional information: This version is the author accepted manuscript. For information on re-use, please refer to the publisher’s terms and conditions.
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/1546708
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