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2 results

Compactness of embeddings of function spaces on quasi-bounded domains and the distribution of eigenvalues of related elliptic operators
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Hans-Gerd Leopold, Leszek Skrzypczak
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Proceedings of the Edinburgh Mathematical Society / Volume 56 / Issue 3 / October 2013

Published online by Cambridge University Press:

10 July 2013, pp. 829-851
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We prove sufficient and necessary conditions for compactness of the Sobolev embeddings of Besov and Triebel–Lizorkin spaces defined on bounded and unbounded uniformly E-porous domains. The asymptotic behaviour of the corresponding entropy numbers is calculated. Some applications to the spectral properties of elliptic operators are described.

!ENTROPY NUMBERS OF EMBEDDINGS OF WEIGHTED BESOV SPACES. II
Thomas Kühn, Hans-Gerd Leopold, Winfried Sickel, Leszek Skrzypczak
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Proceedings of the Edinburgh Mathematical Society / Volume 49 / Issue 2 / June 2006

Published online by Cambridge University Press:

30 May 2006, pp. 331-359
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We investigate the asymptotic behaviour of the entropy numbers of the compact embedding $B^{s_1}_{p_1,q_1}(\mathbb{R}^d,w_1)\hookrightarrow B^{s_2}_{p_2,q_2}(\mathbb{R}^d,w_2)$. Here $B^s_{p,q}(\mathbb{R}^d,w)$ denotes a weighted Besov space. We present a general approach which allows us to work with a large class of weights.

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2 results

Compactness of embeddings of function spaces on quasi-bounded domains and the distribution of eigenvalues of related elliptic operators

!ENTROPY NUMBERS OF EMBEDDINGS OF WEIGHTED BESOV SPACES. II