Titlebook: Sobolev Spaces in Mathematics II; Applications in Anal Vladimir Maz‘ya Book 2009 Springer-Verlag New York 2009 Boundary value problem.Poten

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Function Spaces on Cellular Domains,A Lipschitz domain in R. is called . if it is the finite union of diffeomorphic images of cubes. Bounded C∞ domains and cubes are prototypes. The paper deals with spaces of type ... and ... (including Sobolev spaces and Besov spaces) on these domains. Special attention is paid to traces on (maybe nonsmooth) boundaries and wavelet bases.

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1571-5485 ticles on the works of Sobolev in the 1930s and the foundation of Akademgorodok in Siberia, supplied with unique archive photos of S. Sobolev are included..978-1-4419-2758-3978-0-387-85650-6Series ISSN 1571-5485 Series E-ISSN 1574-8944

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Spectral Stability of Higher Order Uniformly Elliptic Operators,stimate is obtained in terms of the lower Hausdorff—Pompeiu deviation of the boundaries, which in general may be much smaller than the usual Hausdorff—Pompeiu distance. Finally, in the case of diffeomorphic open sets, we obtain an estimate even without the assumption of continuity of the boundaries.

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Variational Approach to Complicated Similarity Solutions of Higher Order Nonlinear Evolution Partiaods, we prove that Eqs. (1) admit an infinite at least countable set of countable families of compactly supported solutions that are oscillatory near finite interfaces. This shows typical properties of a set of solutions of chaotic structure.