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RESEARCH PRODUCT
Spatial Besov regularity for stochastic partial differential equations on Lipschitz domains
Klaus RitterRené L. SchillingFelix LindnerStephan DahlkeThorsten RaaschStefan KinzelPetru A. Cioicasubject
Mathematics::Functional AnalysisSmoothness (probability theory)General MathematicsProbability (math.PR)Mathematics::Analysis of PDEsScale (descriptive set theory)Numerical Analysis (math.NA)Lipschitz continuitySobolev spaceStochastic partial differential equation60H15 Secondary: 46E35 65C30WaveletRate of convergenceBounded functionFOS: MathematicsApplied mathematicsMathematics - Numerical AnalysisMathematics - ProbabilityMathematicsdescription
We use the scale of Besov spaces B^\alpha_{\tau,\tau}(O), \alpha>0, 1/\tau=\alpha/d+1/p, p fixed, to study the spatial regularity of the solutions of linear parabolic stochastic partial differential equations on bounded Lipschitz domains O\subset R^d. The Besov smoothness determines the order of convergence that can be achieved by nonlinear approximation schemes. The proofs are based on a combination of weighted Sobolev estimates and characterizations of Besov spaces by wavelet expansions.
| year | journal | country | edition | language |
|---|---|---|---|---|
| 2010-11-08 | Studia Mathematica |