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On the weak solution of the Neumann problem for the 2D Helmholtz equation in a convex cone and Hs regularity

✍ Scribed by A. E. Merzon; F.-O. Speck; T. J. Villalba-Vega

Publisher: John Wiley and Sons
Year: 2010
Tongue: English
Weight: 312 KB
Volume: 34
Category: Article
ISSN: 0170-4214
DOI: 10.1002/mma.1326

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✦ Synopsis

We extend previous results for the Neumann boundary value problem to the case of boundary data from the space H -1 2 +e (C), 0<e< 1 2 , where C = *X is the boundary of a two-dimensional cone X with angle b<p. We prove that for these boundary conditions the solution of the Helmholtz equation in X exists in the Sobolev space H 1+e (X), is unique and depends continuously on the boundary data. Moreover, we give the Sommerfeld representation for these solutions. This can be used to formulate explicit compatibility conditions on the data for regularity properties of the corresponding solution.

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