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Title: An application of eigenfunctions of $p$-Laplacians to domain separation (English)
Author: Gajewski, Herbert
Language: English
Journal: Mathematica Bohemica
ISSN: 0862-7959 (print)
ISSN: 2464-7136 (online)
Volume: 126
Issue: 2
Year: 2001
Pages: 395-401
Summary lang: English
Category: math
Summary: We are interested in algorithms for constructing surfaces $\Gamma $ of possibly small measure that separate a given domain $\Omega $ into two regions of equal measure. Using the integral formula for the total gradient variation, we show that such separators can be constructed approximatively by means of sign changing eigenfunctions of the $p$-Laplacians, $p \rightarrow 1$, under homogeneous Neumann boundary conditions. These eigenfunctions turn out to be limits of steepest descent methods applied to suitable norm quotients. (English)
Keyword: perimeter
Keyword: relative isoperimetric inequality
Keyword: $p$-Laplacian
Keyword: eigenfunctions
Keyword: steepest decent method
MSC: 35J20
MSC: 35P30
MSC: 58E12
idZBL: Zbl 0979.35041
idMR: MR1844277
DOI: 10.21136/MB.2001.134019
Date available: 2009-09-24T21:51:50Z
Last updated: 2020-07-29
Stable URL:
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