On the solvability of degenerate stochastic partial differential equations in sobolev spaces

Máté Gerencsér; István Gyöngy; Nicolai Krylov

doi:10.1007/s40072-014-0042-6

On the solvability of degenerate stochastic partial differential equations in sobolev spaces

Máté Gerencsér, István Gyöngy, Nicolai Krylov

School of Mathematics

Research output: Contribution to journal › Article › peer-review

19 Scopus citations

Abstract

Systems of parabolic, possibly degenerate parabolic SPDEs are considered. Existence and uniqueness are established in Sobolev spaces. Similar results are obtained for a class of equations generalizing the deterministic first order symmetric hyperbolic systems.

Original language	English (US)
Pages (from-to)	52-83
Number of pages	32
Journal	Stochastics and Partial Differential Equations: Analysis and Computations
Volume	3
Issue number	1
DOIs	https://doi.org/10.1007/s40072-014-0042-6
State	Published - Mar 2015

Bibliographical note

Funding Information:
The results of this paper were presented at the 9th International Meeting on “Stochastic Partial Differential Equations and Applications” in Levico Terme in Italy, in January, 2014, and at the meeting on “Stochastic Processes and Differential Equations in Infinite Dimensional Spaces” in King’s College London, in March, 2014. The authors would like to thank the organisers for these possibilities. The authors are grateful to the referee whose comments and suggestions helped to improve the presentation of the paper. The work of the third author was partially supported by NSF Grant DMS-1160569.

Publisher Copyright:
© Springer Science+Business Media New York 2014.

Keywords

Cauchy problem
Degenerate stochastic parabolic PDEs
First order symmetric hyperbolic system

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10.1007/s40072-014-0042-6

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abstract = "Systems of parabolic, possibly degenerate parabolic SPDEs are considered. Existence and uniqueness are established in Sobolev spaces. Similar results are obtained for a class of equations generalizing the deterministic first order symmetric hyperbolic systems.",

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AU - Gyöngy, István

AU - Krylov, Nicolai

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KW - Cauchy problem

KW - Degenerate stochastic parabolic PDEs

KW - First order symmetric hyperbolic system

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On the solvability of degenerate stochastic partial differential equations in sobolev spaces

Abstract

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