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Existence and uniqueness results for a non linear stochastic partial differential equation

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Stochastic Partial Differential Equations and Applications

Part of the book series: Lecture Notes in Mathematics ((LNM,volume 1236))

Abstract

We study the non linear stochastic partial differential equation \(du(t,x) = A(x,u,Du,D''u)dt + (\sum\limits_{j = 1}^n {G_j (x)D_j u(t,x) + h(x,u(t,x))dW(t)} \)where A is a convex functional and W(t) a real Wiener process. We study the corresponding non linear robust equation by linearization methods. We also prove some existence and uniqueness results for parabolic equations with unbounded coefficients in Hölder spaces.

The A.A. are members of G.N.A.F.A. (C.N.R.). This work is partially supported by the Research Funds of the Ministero della Pubblica Istruzione

The A. is presently on duty at Stato Maggiore Marina, Palazzo Marina, Rome

This A. held the present communication at Trento

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Author information

Authors and Affiliations

  1. Gruppo Insegnamento Matematiche, Accademia Navale, 57100, Livorno, Italy

    Piermarco Cannarsa

  2. Dipartimento di Matematica, II Università di Roma Via O. Raimondo, Roma, Italy

    Vincenzo Vespri

Authors
  1. Piermarco Cannarsa
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  2. Vincenzo Vespri
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Editor information

Giuseppe Da Prato Luciano Tubaro

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© 1987 Springer-Verlag

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Cannarsa, P., Vespri, V. (1987). Existence and uniqueness results for a non linear stochastic partial differential equation. In: Da Prato, G., Tubaro, L. (eds) Stochastic Partial Differential Equations and Applications. Lecture Notes in Mathematics, vol 1236. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0072880

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  • DOI: https://doi.org/10.1007/BFb0072880

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-17211-6

  • Online ISBN: 978-3-540-47408-1

  • eBook Packages: Springer Book Archive

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