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Imbedding theorems for Sobolev spaces on domains with peak and on Hölder domains


Authors: V. G. Maz'ya and S. V. Poborchi
Translated by: S. V. Poborchi
Original publication: Algebra i Analiz, tom 18 (2006), nomer 4.
Journal: St. Petersburg Math. J. 18 (2007), 583-605
MSC (2000): Primary 46E35
DOI: https://doi.org/10.1090/S1061-0022-07-00962-4
Published electronically: May 29, 2007
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Abstract | References | Similar Articles | Additional Information

Abstract: Necessary and sufficient conditions are obtained for the continuity and compactness of the imbedding operators $ W_p^l(\Omega)\to L_q(\Om)$ and $ W_p^l(\Omega)\to C(\Omega)\cap L_\infty(\Omega)$ for a domain with an outward peak. More simple sufficient conditions are presented. Applications to the solvability of the Neumann problem for elliptic equations of order $ 2l$, $ l\ge1$, for a domain with peak are given. An imbedding theorem for Sobolev spaces on Hölder domains is stated.


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Additional Information

V. G. Maz'ya
Affiliation: Department of Mathematics, 581 83 Linköping University, Sweden
Email: vlmaz@mai.liu.se

S. V. Poborchi
Affiliation: Department of Mathematics and Mechanics, St. Petersburg State University, Universitetskiĭ Prospect 28, Staryĭ Peterhof, St. Petersburg 198504, Russia
Email: Sergei.Poborchi@paloma.spbu.ru

DOI: https://doi.org/10.1090/S1061-0022-07-00962-4
Keywords: Sobolev spaces, imbedding theorems, irregular boundary, domain with peak
Received by editor(s): September 5, 2005
Published electronically: May 29, 2007
Article copyright: © Copyright 2007 American Mathematical Society