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2014 Maximum principle for quasilinear stochastic PDEs with obstacle
Laurent Denis, Anis Matoussi, Jing Zhang
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Electron. J. Probab. 19: 1-32 (2014). DOI: 10.1214/EJP.v19-2716

Abstract

We prove a maximum principle for local solutions of quasi linear stochastic PDEs with obstacle (in short OSPDE). The proofs are based on a version of Ito's formula and estimates for the positive part of a local solution which is non-positive on the lateral boundary.

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Laurent Denis. Anis Matoussi. Jing Zhang. "Maximum principle for quasilinear stochastic PDEs with obstacle." Electron. J. Probab. 19 1 - 32, 2014. https://doi.org/10.1214/EJP.v19-2716

Information

Accepted: 12 May 2014; Published: 2014
First available in Project Euclid: 4 June 2016

zbMATH: 1310.60093
MathSciNet: MR3210545
Digital Object Identifier: 10.1214/EJP.v19-2716

Subjects:
Primary: 60H15
Secondary: 31B150 , 35R60

Keywords: $L^p-$estimate , Comparison theorem , It\^o's formula , local solution , maximum principle , Moser iteration , obstacle problems , Stochastic PDE's

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