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Multiple Layer Potentials for General Elliptic Boundary Value Problems in a Quadrant or Its Exterior by Günter Albinus is a Mathematics article available to read on EtoBox.

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By GUNTER ALBINUS in Berlin (Eingegangen a m 29. 4.1980) 0. Introduction. The author [3] has modified S. AGMON'S [l] multiple layer potentials for homogeneous linear elliptic differential operators in the plane, in order to apply the potentials to the DIRICHLET problem in a bounded simply connected domain whose boundary is piecewise smooth only. The results of [3] have been applied by A.-M. SANDIG [lo] to prove apriori estimates in C1 norms for biharmonic functions in a rectangle. In this paper we shall define multiple layer potentials for general elliptic boundary value problems for homogeneous linear elliptic operators of order 2p with real constant coefficients in the quadrant and in its exterior and we shall discuss the systems of integral equations which arise. Since the quadrant and its exterior may play the same role for boundary value problems in plane domains whose boundary is piecewise smooth as the halfspace does play for domains with smooth boundaries (cf. [2]), we hope to deal with general elliptic boundafy value problems in plane domains with a piecewise smooth boundary in a forthcoming paper. We shall also use essentially the fact that we work in two dimensions only.

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Author

Günter Albinus

Publisher

John Wiley and Sons; Wiley (John Wiley & Sons); Wiley - V C H Verlag GmbbH & Co.; Wiley (ISSN 0025-584X)

Published

1980

Language

EN

Field

Mathematics (Physical Sciences)