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Lp estimates for the uniform norm of solutions of quasilinear SPDE's
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  • Published: 03 May 2005

Lp estimates for the uniform norm of solutions of quasilinear SPDE's

  • Laurent Denis1,
  • Anis Matoussi2 &
  • Lucretiu Stoica3 

Probability Theory and Related Fields volume 133, pages 437–463 (2005)Cite this article

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  • 32 Citations

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Abstract

In this paper we prove Lp 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.

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Authors and Affiliations

  1. Département de Mathématiques, Equipe “Analyse et Probabilités”, Université d'Evry-Val-d'Essonne, Boulevard F. Mitterrand, 91 025, EVRY Cedex, France

    Laurent Denis

  2. Département de Mathématiques, Equipe “Statistique et Processus”, Université du Maine, Avenue Olivier Messiaen, 72085, LE MANS Cedex 9, France

    Anis Matoussi

  3. Faculty of Mathematics, University of Bucharest, Str. Academiei 14, Bucharest, RO, 70109, Romania

    Lucretiu Stoica

Authors
  1. Laurent Denis
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  2. Anis Matoussi
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  3. Lucretiu Stoica
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Corresponding author

Correspondence to Laurent Denis.

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Denis, L., Matoussi, A. & Stoica, L. Lp estimates for the uniform norm of solutions of quasilinear SPDE's. Probab. Theory Relat. Fields 133, 437–463 (2005). https://doi.org/10.1007/s00440-005-0436-5

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  • Received: 24 July 2003

  • Revised: 31 January 2005

  • Published: 03 May 2005

  • Issue Date: December 2005

  • DOI: https://doi.org/10.1007/s00440-005-0436-5

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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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