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Spatial Besov regularity for stochastic partial differential equations on Lipschitz domains

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Cioica P., Dahlke S., Kinzel S., Lindner F., Raasch T., Ritter K., Schilling R.

Studia Mathematica

2011

tom 207

nr 3

197-234

We use the scale of Besov spaces $B^{α}_{τ,τ}(𝓞)$, 1/τ = α/d + 1/p, α > 0, p fixed, to study the spatial regularity of solutions of linear parabolic stochastic partial differential equations on bounded Lipschitz domains 𝓞 ⊂ ℝ. 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.

Ograniczanie wyników

1 Studia Mathematica

1 Cioica P.

1 Dahlke S.

1 Kinzel S.

1 Lindner F.

1 Raasch T.

1 Ritter K.

1 Schilling R.

1 2011

Wyniki wyszukiwania

Spatial Besov regularity for stochastic partial differential equations on Lipschitz domains