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Parabolic SPDEs degenerating on the boundary of non-smooth domain
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Kyeong-Hun Kim, Korea University |
Abstract
Degenerate stochastic partial differential equations of divergence and non-divergence forms are considered
in non-smooth domains. Existence and uniqueness results are given in weighted Sobolev spaces, and H"older estimates of the solutions are presented.
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Full text: PDF
Pages: 563-584
Published on: August 2, 2006
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Bibliography
- Aronson, D. G.; Besala, P. Parabolic equations with unbounded coefficients.
J. Differential Equations 3 1967 1--14. MR0208160 (34 #7970)
- Gilbarg, David; Trudinger, Neil S. Elliptic partial differential equations of second order.
of Mathematical Sciences], 224. Springer-Verlag, Berlin, 1983. xiii+513 pp. ISBN: 3-540-13025-X MR0737190 (86c:35035)
- Kim, Kyeong-Hun. On stochastic partial differential equations with variable
Stochastic Process. Appl. 112 (2004), no. 2, 261--283. MR2073414 (2005e:60128)
- Kim, Kyeong-Hun. On $Lsb p$-theory of stochastic partial differential equations of
Probab. Theory Related Fields 130 (2004), no. 4, 473--492. MR2102888 (2005h:60185)
- K. Kim and N.V. Krylov, On stochastic partial
differential equations with variable coefficients in one
dimension,
Potential Anal., 21 (2004), no.3, 203-239.
- Kim, Kyeong-Hun; Krylov, N. V. On the Sobolev space theory of parabolic and elliptic equations in
SIAM J. Math. Anal. 36 (2004), no. 2, 618--642 (electronic). MR2111792 (2005k:35168)
- Krylov, N. V. Some properties of traces for stochastic and deterministic parabolic
J. Funct. Anal. 183 (2001), no. 1, 1--41. MR1837532 (2002c:46069)
- Krylov, N. V. An analytic approach to SPDEs.
185--242, Math. Surveys Monogr., 64, Amer. Math. Soc., Providence, RI, 1999. MR1661766 (99j:60093)
- Krylov, N. V. Weighted Sobolev spaces and Laplace's equation and the heat equations
Comm. Partial Differential Equations 24 (1999), no. 9-10, 1611--1653. MR1708104 (2000j:46065)
- Krylov, N. V.; Lototsky, S. V.. A Sobolev space theory of SPDEs with constant coefficients in a half
SIAM J. Math. Anal. 31 (1999), no. 1, 19--33 (electronic). MR1720129 (2001a:60072)
- O.A. Ladyzhenskaya, V.A. Solonnikov, and N.N.
Utal'stseva, Linear and quasilinear parabolic equations, Am.
Math.Soc. (1968).
- Lototsky, S. V.. Linear stochastic parabolic equations, degenerating on the boundary of
Electron. J. Probab. 6 (2001), no. 24, 14 pp. (electronic). MR1873301 (2002j:60114)
- Lototsky, S. V.. Sobolev spaces with weights in domains and boundary value problems for
Methods Appl. Anal. 7 (2000), no. 1, 195--204. MR1796011 (2001m:46077)
- Lototsky, Sergey V.. Dirichlet problem for stochastic parabolic equations in smooth
Stochastics Stochastics Rep. 68 (1999), no. 1-2, 145--175. MR1742721 (2000i:60069)
- R. Mikulevicius and B. Rozovskii, A note on
Krylov's $L_p$-theory for systems of SPDEs, Electron. J. Probab.,
6 (2001), no. 12, 35 pp.
- Oleinik, O. A.; Radkevic, E. V. Second order equations with nonnegative characteristic form.
Plenum Press, New York-London, 1973. vii+259 pp. ISBN: 0-306-30751-0 MR0457908 (56 #16112)
- Pardoux, E. Stochastic partial differential equations and filtering of diffusion
Stochastics 3, no. 2, 127--167. (1979), MR0553909 (81b:60059)
- Pukal'skii, I. D. Estimates of the solutions of parabolic equations that are degenerate
(Russian) Mat. Zametki 22 (1977), no. 4, 553--560. MR0509709 (58 #23068)
- Triebel, Hans. Interpolation theory, function spaces, differential operators.
Johann Ambrosius Barth, Heidelberg, 1995. 532 pp. ISBN: 3-335-00420-5 MR1328645 (96f:46001)
- Visik, M. I.; Grusin, V. V. Boundary value problems for elliptic equations which are degenerate on
(Russian) Mat. Sb. (N.S.) 80 (122) 1969 455--491. MR0257562 (41 #2212)
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Electronic Journal of Probability. ISSN: 1083-6489 |
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