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title:
Adaptive Wavelet Methods for SPDEs II: Regularity Results for Parabolic Equations |
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name:
Lindner |
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first name:
Felix
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location/conference:
SPP-JT11
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PRESENTATION-link:
http://www.dfg-spp1324.de/nuhagtools/event_NEW/dateien/SPP-JT11/talks/SPP-JT2011_09_lindner.pdf |
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abstract:
We present recent regularity results for SPDEs of parabolic type which are closely connected to the question wether adaptive approximation methods pay off in the sense that they admit better convergence rates than uniform approximation methods. Our result concering the spatial Besov regularity for linear parabolic SPDEs on Lipschitz domains has been improved with respect to Hölder regularity in time, and a result concerning the spatial Besov regularity for semilinear equations has been obtained. We also show that the solution to the stochastic heat equation on a non-convex polygonal domain can be decomposed into a regular part and an irregular part restricting the convergence rates of uniform approximation methods. |
