The obstacle problem for quasilinear stochastic PDEs with non-homogeneous operator - Archive ouverte HAL
Article Dans Une Revue Discrete and Continuous Dynamical Systems - Series A Année : 2015

The obstacle problem for quasilinear stochastic PDEs with non-homogeneous operator

Laurent Denis
Anis Matoussi
Jing Zhang
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Résumé

We prove the existence and uniqueness of solution of the obstacle problem for quasilinear Stochastic PDEs with non-homogeneous second order operator. Our method is based on analytical technics coming from the parabolic potential theory. The solution is expressed as a pair (u, v) where u is a predictable continuous process which takes values in a proper Sobolev space and v is a random regular measure satisfying minimal Skohorod condition. Moreover, we establish a maximum principle for local solutions of such class of stochastic PDEs. The proofs are based on a version of Itô's formula and estimates for the positive part of a local solution which is non-positive on the lateral boundary.

Dates et versions

hal-03687270 , version 1 (03-06-2022)

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Citer

Laurent Denis, Anis Matoussi, Jing Zhang. The obstacle problem for quasilinear stochastic PDEs with non-homogeneous operator. Discrete and Continuous Dynamical Systems - Series A, 2015, 35 (11), pp.5185-5202. ⟨10.3934/dcds.2015.35.5185⟩. ⟨hal-03687270⟩

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