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- W2724953914 abstract "We investigate the Besov regularity for solutions of elliptic PDEs. This is based on regularity results in Babuska---Kondratiev spaces. Following the argument of Dahlke and DeVore, we first prove an embedding of these spaces into the scale $$B^r_{tau ,tau }(D)$$B?,?r(D) of Besov spaces with $$frac{1}{tau }=frac{r}{d}+frac{1}{p}$$1?=rd+1p. This scale is known to be closely related to $$n$$n-term approximation w.r.t. wavelet systems, and also adaptive finite element approximation. Ultimately, this yields the rate $$n^{-r/d}$$n-r/d for $$uin {mathcal {K}}^m_{p,a}(D)cap H^s_p(D)$$u?Kp,am(D)?Hps(D) for $$rfrac{1}{tau }ge frac{1}{p}$$md+1p>1??1p, which in turn indeed yields the desired $$n$$n-term rate. As an intermediate step, we also prove an extension theorem for Kondratiev spaces." @default.
- W2724953914 created "2017-07-14" @default.
- W2724953914 creator A5036122196 @default.
- W2724953914 date "2014-01-01" @default.
- W2724953914 modified "2023-09-24" @default.
- W2724953914 title "Nonlinear Approximation Rates and Besov Regularity for Elliptic PDEs on Polyhedral Domains" @default.
- W2724953914 doi "https://doi.org/10.3929/ethz-a-010386351" @default.
- W2724953914 hasPublicationYear "2014" @default.
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