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Stochastic Porous Media Equations pp 95–106Cite as

Variational Approach to Stochastic Porous Media Equations

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Part of the book series: Lecture Notes in Mathematics ((LNM,volume 2163))

Abstract

We shall briefly present here a different approach to stochastic porous media equations which in analogy to the variational formulation of parabolic boundary value problems will be called variational approach. It is based on a general existence result for infinite dimensional stochastic equations of the form

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References

  1. R. Adams, Sobolev Spaces (Academic Press, San Francisco, 1975)

    MATH  Google Scholar 

  2. V. Barbu, M. Röckner, An operatorial approach to stochastic partial differential equations driven by linear multiplicative noise. J. Eur. Math, Soc. 17, 1789–1815 (2015)

    Google Scholar 

  3. H. Brezis, Functional Analysis, Sobolev Spaces and Partial Differential Equations (Springer, New York, 2010)

    Book  Google Scholar 

  4. N. Krylov, B.L. Rozovskii, Stochastic evolution equations. J. Sov. Math. 16, 1233–1277 (1981)

    Article  MATH  Google Scholar 

  5. W. Liu, M. Röckner, Stochastic Partial Differential Equations: An Introduction. Universitext. (Springer, Cham, 2015)

    Google Scholar 

  6. E. Pardoux, Équations aux dérivées partielle stochastiques nonlineaires monotones, Thèse, Paris, 1972

    MATH  Google Scholar 

  7. C. Prevot, M. Röckner, A Concise Course on Stochastic Partial Differential Equations. Lecture Notes in Mathematics, vol. 1905 (Springer, Berlin, 2007)

    Google Scholar 

  8. J. Ren, M. Röckner, F.Y. Wang, Stochastic generalized porous media and fast diffusion equations. J. Differ. Equ. 238 (1), 118–152 (2007)

    Article  MathSciNet  MATH  Google Scholar 

  9. M. Röckner, F.Y. Wang, Non-monotone stochastic generalized porous media equations. J. Differ. Equ. 245 (12), 3898–3935 (2008)

    Article  MathSciNet  MATH  Google Scholar 

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Author information

Authors and Affiliations

  1. Department of Mathematics, Al. I. Cuza University & Octav Mayer Institute of Mathematics of the Romanian Academy, Iasi, Romania

    Viorel Barbu

  2. Classe di Scienze, Scuola Normale Superiore di Pisa, Pisa, Italy

    Giuseppe Da Prato

  3. Department of Mathematics, University of Bielefeld, Bielefeld, Germany

    Michael Röckner

Authors
  1. Viorel Barbu
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  2. Giuseppe Da Prato
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  3. Michael Röckner
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Barbu, V., Da Prato, G., Röckner, M. (2016). Variational Approach to Stochastic Porous Media Equations. In: Stochastic Porous Media Equations. Lecture Notes in Mathematics, vol 2163. Springer, Cham. https://doi.org/10.1007/978-3-319-41069-2_4

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