L p -theory of parabolic SPDEs degenerating on the boundary of C 1 domains

Journal of Theoretical Probability

Volumn 21, Issue 1, 2008, Pages 169-192

  Kim, Kyeong Hun ^a  

^a Korea University   (South Korea)

Author keywords

SPDEs degenerating on the boundary; Weighted Sobolev spaces

Indexed keywords

EID: 38349172389     PISSN: 08949840     EISSN: 15729230     Source Type: Journal    
DOI: 10.1007/s10959-007-0098-6     Document Type: Article

References (19)

1. Aronson, D.G., Besala, P.: Parabolic equations with unbounded coefficients. J. Differ. Equ. 3, 1-14 (1967)
2. p ) theory and Hölder estimates for parabolic SPDE. Stoch. Process. Appl. 114, 313-330 (2004)
3. 1 domains. Stoch. Process. Appl. 112, 261-283 (2004)
4. Kim, K.: Parabolic SPDEs generating on the boundary of non-smooth domain. Electron. J. Probab. 11, 563-584 (2006)
5. 1 domains. SIAM J. Math. Anal. 36, 618-642 (2004)
6. Krylov, N.V.: An analytic approach to SPDEs. In: Stochastic Partial Differential Equations: Six Perspectives. Mathematical Surveys and Monographs, vol. 64, pp. 185-242. AMS, Providence (1999)
7. Krylov, N.V.: Weighted Sobolev spaces and Laplace equations and the heat equations in a half space. Comm. Partial Differ. Equ. 23, 1611-1653 (1999)
8. Krylov, N.V.: Some properties of traces for stochastic and deterministic parabolic weighted Sobolev spaces. J. Funct. Anal. 183, 1-41 (2004)
9. Krylov, N.V., Lototsky, S.V.: A Sobolev space theory of SPDEs with constant coefficients in a half space. SIAM J. Math. Anal. 31, 19-33 (1999)
10. Ladyzhenskaya, O.A., Solonnikov, V.A., Utal'stseva, N.N.: Linear and Quasilinear Parabolic Equations. Am. Math. Soc., Providence (1968)
11. Lototsky, S.V.: Dirichlet problem for stochastic parabolic equations in smooth domains. Stoch. Stoch. Rep. 68, 145-175 (1999)
12. Lototsky, S.V.: Sobolev spaces with weights in domains and boundary value problems for degenerate elliptic equations. Methods Appl. Anal. 1, 195-204 (2000)
13. Lototsky, S.V.: Linear stochastic parabolic equations, degenerating on the boundary of a domain. Electron. J. Probab. 6, 1-14 (2001)
14. p -theory for systems of SPDEs. Electron. J. Probab. 6, 1-35 (2001)
15. Oleinik, O.A., Radkevič, E.V.: Second Order Equations with Nonnegative Characteristic Form. AMS and Plenum, New York (1973)
16. Pardoux, E.: Stochastic partial differential equations and filtering of diffusion processes. Stochastics 3, 127-167 (1979)
17. Pukal'skii, I.D.: Estimates of solutions of parabolic equations degenerating on the boundary of a domain. Mathematical Notes 22 (Historical Archive), 799-803 (1977)
18. Triebel, H.: Interpolation Theory, Function Spaces, Differential Operators. Johann Amrosius Barth, Heidelberg (1995)
19. Višik, M.I., Grušin, V.V.: Boundary value problems for elliptic equations which are degenerate on the boundary of the domain. Math. USSR Sb. 9, 423-454 (1969)