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On Solvability of the Neumann Problem in an Energy Space for a Domain with Peak

On Solvability of the Neumann Problem in an Energy Space for a Domain with Peak We describe the dual space of the boundary trace space for functions with a finite Dirichlet integral for a domain with a vertex of an isolated cusp at the boundary. This leads to conditions of solvability of the Neumann problem for elliptic equations of second order. In particular, we give an explicit necessary and sufficient condition for 𝑞 such that the Neumann problem is solvable if the boundary function is in 𝐿 𝑞 over the boundary of a domain with an outer peak. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Georgian Mathematical Journal de Gruyter

On Solvability of the Neumann Problem in an Energy Space for a Domain with Peak

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Publisher
de Gruyter
Copyright
© Heldermann Verlag
ISSN
1072-947X
eISSN
1072-9176
DOI
10.1515/GMJ.2007.499
Publisher site
See Article on Publisher Site

Abstract

We describe the dual space of the boundary trace space for functions with a finite Dirichlet integral for a domain with a vertex of an isolated cusp at the boundary. This leads to conditions of solvability of the Neumann problem for elliptic equations of second order. In particular, we give an explicit necessary and sufficient condition for 𝑞 such that the Neumann problem is solvable if the boundary function is in 𝐿 𝑞 over the boundary of a domain with an outer peak.

Journal

Georgian Mathematical Journalde Gruyter

Published: Sep 1, 2007

Keywords: Traces of Sobolev functions; irregular domains; Neumann problem

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