Besov Regularity for Second Order Elliptic Boundary Value Problems with Variable Coefficients.
Continous Wavelet Transforms with Applications to Analyzing Functions on Spheres.
Adaptive wavelet methods for saddle point problems
Adaptive wavelet methods for saddle point problems
Recently, adaptive wavelet strategies for symmetric, positive definite operators have been introduced that were proven to converge. This paper is devoted to the generalization to saddle point problems which are also symmetric, but indefinite. Firstly, we investigate error estimates and generalize the known adaptive wavelet strategy to saddle point problems. The convergence of this strategy for elliptic operators essentially relies on the positive definite character of the operator. As an alternative,...
Spatial Besov regularity for stochastic partial differential equations on Lipschitz domains
We use the scale of Besov spaces , 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 ⊂ 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.
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