✦ LIBER ✦

The jump problem for the laplace equation

✍ Scribed by P.A. Krutitskii

Publisher: Elsevier Science
Year: 2001
Tongue: English
Weight: 471 KB
Volume: 14
Category: Article
ISSN: 0893-9659
DOI: 10.1016/s0893-9659(00)00161-0

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✦ Synopsis

The boundary value problem for the Laplace equation outside several cuts in a plane is studied. The jump of the solution of the Laplace equation and the jump of its normal derivative are specified of the cuts. The problem is studied under different conditions at infinity, which lead to different uniqueness and existence theorems. The solution of this problem is constructed in the explicit form by means of single-layer and angular potentials. The singularities at the ends of the cuts are investigated.

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