Weak solutions to stochastic porous media equations

Journal of Evolution Equations

Volumn 4, Issue 2, 2004, Pages 249-271

  Da Prato, Giuseppe ^a   Röckner, Michael ^b  

^a SCUOLA NORMALE SUPERIORE   (Italy)

^b BIELEFELD UNIVERSITY   (Germany)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 2942532492     PISSN: 14243199     EISSN: None     Source Type: Journal    
DOI: 10.1007/s00028-003-0140-9     Document Type: Article

References (13)

1. ARONSON, D. G., The porous medium equation, in Lect. Notes Math. vol. 1224, (A. Fasano and al. editors), Springer, Berlin. 1986 1-46.
2. BARBU, V., Analysis and control of nonlinear infinite dimensional systems, Academic Press, San Diego. 1993.
3. BARBU, V. and DA PRATO, G., The two phase stochastic Stefan problem, Probab. Theory Relat. Fields, 124 (2002), 544-560.
4. BOGACHEV, V. and RÖCKNER, M., Elliptic equations for measures on infinite dimensional spaces and applications, Probab. Theory Relat. Fields, 120 (2001), 445-496.
5. DA PRATO, G. and RÖCKNER, M., Singular dissipative stochastic equations in Hilbert spaces, Probab. Theory Relat. Fields, 124 (2002) no. 2, 261-303.
6. DA PRATO, G. and RÖCKNER, M., Invariant measures for a stochastic porous medium equation, preprint SNS, 2003.
7. EBERLE, A., Uniqueness and non-uniqueness of singular diffusion operators, Lecture Notes in Mathematics 1718, Berlin, Springer-Verlag, 1999.
8. FUKUSHMA, M., OSHMA, Y. and TAKEDA, M., Dirichlet forms and symmetric Markov processes, de Gruyter, Berlin, 1994.
9. MA, Z. M. and RÖCKNER, M., Introduction to the Theory of (Non Symmetric) Dirichlet Forms, Springer-Verlag, 1992.
10. p-analysis of finite and infinite dimensional diffusions, Lecture Notes in Mathematics, 1715, G. Da Prato (editor), Springer-Verlag, 1999, 65-116.
11. RÖCKNER, M. and SOBOL, Z., Generalized stochastic Burgers equations: regularity theory for their Kolmogorov operators, preprint 2003.
12. STANNAT, W., The theory of generalized Dirichlet forms and its Applications in Analysis and Stochastics, Memoirs AMS, 678, 1999.
13. STROOCK, D. W. and VARADHAN, S. R. S., Multidimensional Diffusion Processes, Springer-Verlag, 1979.