An application of eigenfunctions of $p$-Laplacians to domain separation

@article{Gajewski2001,
abstract = {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.},
author = {Gajewski, Herbert},
journal = {Mathematica Bohemica},
keywords = {perimeter; relative isoperimetric inequality; $p$-Laplacian; eigenfunctions; steepest decent method; perimeter; relative isoperimetric inequality; -Laplacian; eigenfunctions; steepest decent method},
language = {eng},
number = {2},
pages = {395-401},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {An application of eigenfunctions of $p$-Laplacians to domain separation},
url = {http://eudml.org/doc/248826},
volume = {126},
year = {2001},
}

TY - JOUR
AU - Gajewski, Herbert
TI - An application of eigenfunctions of $p$-Laplacians to domain separation
JO - Mathematica Bohemica
PY - 2001
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 126
IS - 2
SP - 395
EP - 401
AB - 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.
LA - eng
KW - perimeter; relative isoperimetric inequality; $p$-Laplacian; eigenfunctions; steepest decent method; perimeter; relative isoperimetric inequality; -Laplacian; eigenfunctions; steepest decent method
UR - http://eudml.org/doc/248826
ER -