On the Well-Posedness of SPDEs with Singular Drift in Divergence Form

  • Carlo Marinelli
  • Luca ScarpaEmail author
Conference paper
Part of the Springer Proceedings in Mathematics & Statistics book series (PROMS, volume 229)


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 \({\mathrm {div}}\gamma (\nabla \cdot )\), where \(\gamma \) is a maximal monotone graph in \(\mathbb {R}^n \times \mathbb {R}^n\) obtained 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 \(\gamma \) is single-valued, a solution with better integrability and regularity properties is constructed. The proof given here, however, is self-contained.


Stochastic evolution equations Singular drift Divergence form Multiplicative noise Monotone operators 

2010 Mathematics Subject Classification

Primary: 60H15 47H06 Secondary: 46N30 



The authors are partially supported by The Royal Society through its International Exchange Scheme. Parts of this chapter were written while the first-named author was visiting the Interdisziplinäres Zentrum für Komplexe Systeme at the University of Bonn, hosted by Prof. S. Albeverio.


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Copyright information

© Springer International Publishing AG, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Department of MathematicsUniversity College LondonLondonUK

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