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2002 Higher order Neumann problems for Laplace's equation in two dimensions
Michael Renardy
Differential Integral Equations 15(10): 1273-1279 (2002).

Abstract

We discuss the boundary value problem $\Delta u=f$, $\partial^ku/\partial n^k=g$ in a bounded two-dimensional domain. For a smooth simply connected region, we prove that the only solutions of the homogeneous problem are harmonic polynomials of degree $k-1$. For multiply connected domains, this is true ``generically." In domains with corners, on the other hand, there are additional solutions.

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Michael Renardy. "Higher order Neumann problems for Laplace's equation in two dimensions." Differential Integral Equations 15 (10) 1273 - 1279, 2002.

Information

Published: 2002
First available in Project Euclid: 21 December 2012

zbMATH: 1017.35031
MathSciNet: MR1919772

Subjects:
Primary: 35J05
Secondary: 35J25

Rights: Copyright © 2002 Khayyam Publishing, Inc.

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Vol.15 • No. 10 • 2002
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