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May/June 2015 Uniform convergence of solutions to elliptic equations on domains with shrinking holes
E.N. Dancer, Daniel Daners, Daniel Hauer
Adv. Differential Equations 20(5/6): 463-494 (May/June 2015).

Abstract

We consider solutions of the Poisson equation on a family of domains with holes shrinking to a point. Assuming Robin or Neumann boundary conditions on the boundary of the holes, we show that the solution converges uniformly to the solution of the Poisson equation on the domain without the holes. This is in contrast to Dirichlet boundary conditions where there is no uniform convergence. The results substantially improve earlier results on $L^p$-convergence. They can be applied to semi-linear problems.

Citation

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E.N. Dancer. Daniel Daners. Daniel Hauer. "Uniform convergence of solutions to elliptic equations on domains with shrinking holes." Adv. Differential Equations 20 (5/6) 463 - 494, May/June 2015.

Information

Published: May/June 2015
First available in Project Euclid: 30 March 2015

zbMATH: 1319.35026
MathSciNet: MR3327704

Subjects:
Primary: 35B25, 35B45, 35J25

Rights: Copyright © 2015 Khayyam Publishing, Inc.

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Vol.20 • No. 5/6 • May/June 2015
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