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| Stochastic Partial Differential Equations and the Related Fields. |
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Title |
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Petru A. Cioica |
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2012-06-27 |
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NIMS |
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 Abstract : We analyse the regularity of stochastic partial di erential equations (SPDEs, for short) on bounded Lipschitz domains in a certain scale of Besov spaces, which is closely related to the convergence rate of non-linear approximation methods. We will rst describe this relation in detail. Afterwards, we show how we can exploit the theory of SPDEs in weighted Sobolev spaces, developed by Krylov, Kim, Lototsky and collaborators, for our purposes. In particular we present an embedding of these spaces into the desired scale of Besov spaces. These results pave the way to a rigorous convergence analysis of adaptive wavelet methods for SPDEs. Furthermore, combining them with the results concerning the Sobolev regularity presented in the talk of Felix Lindner, we can expect that adaptive methods will lead to better convergence rates than uniform ones.
(*)This is joint work with S. Dahlke, S. Kinzel, F. Lindner, T. Raasch, K. Ritter, R.L. Schilling as well as K.-H. Kim and K. Lee. |
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