Probability Theory and Related Fields

, Volume 133, Issue 4, pp 437–463 | Cite as

L p estimates for the uniform norm of solutions of quasilinear SPDE's

  • Laurent Denis
  • Anis Matoussi
  • Lucretiu Stoica


In this paper we prove L p estimates (p≥2) for the uniform norm of the paths of solutions of quasilinear stochastic partial differential equations (SPDE) of parabolic type. Our method is based on a version of Moser's iteration scheme developed by Aronson and Serrin in the context of non-linear parabolic PDE.

Mathematics Subject Classifications (2000)

60H15 60G46 35R60 

Key words or phrases

Stochastic partial differential equation Itô's formula Maximum principle Moser's iteration 


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Copyright information

© Springer-Verlag Berlin Heidelberg 2005

Authors and Affiliations

  1. 1.Département de Mathématiques, Equipe “Analyse et Probabilités”Université d'Evry-Val-d'EssonneEVRY CedexFrance
  2. 2.Département de Mathématiques, Equipe “Statistique et Processus”Université du MaineLE MANS Cedex 9France
  3. 3.Faculty of MathematicsUniversity of BucharestBucharestRomania

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