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

Mathematica Bohemica (2001)

- Volume: 126, Issue: 2, page 395-401
- ISSN: 0862-7959

## Access Full Article

top## Abstract

top## How to cite

topGajewski, Herbert. "An application of eigenfunctions of $p$-Laplacians to domain separation." Mathematica Bohemica 126.2 (2001): 395-401. <http://eudml.org/doc/248826>.

@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 -

## References

top- 10.1007/BF01176474, Math. Z. 183 (1983), 311–341. (1983) MR0706391DOI10.1007/BF01176474
- On relative isoperimetric inequalities in the plane, Bollettino U.M.I. 7 (1989), 3–13. (1989) Zbl0674.49030MR0997998
- Degenerate Parabolic Equations, Springer, Basel, 1993. (1993) MR1230384
- Quasilinear Elliptic Equations with Degenerations and Singularities, Walter de Gruyter, Berlin, 1997. (1997) MR1460729
- 10.2307/1970227, Ann. Math. 72 (1960), 458–520. (1960) MR0123260DOI10.2307/1970227
- 10.1007/BF01236935, Arch. Math. 11 (1960), 218–222. (1960) MR0114892DOI10.1007/BF01236935
- 10.1002/zamm.19960760502, Z. Angew. Math. Mech. 76 (1996), 247–264. (1996) MR1390298DOI10.1002/zamm.19960760502
- Domain separation by means of sign changing eigenfunctions of $p$-Laplacians, Preprint No. 526, Weierstraß Institute, Berlin, 1999. (1999) MR1880955
- Nichtlineare Operatorgleichungen ond Operatordifferentialgleichungen, Akademie, Berlin, 1974. (1974) MR0636412
- Elliptic Partial Differential Equations of Second Order, Springer, 1983. (1983) MR0737190
- Minimal Surfaces and Functions of Bounded Variation, Birkhäuser, Basel, 1984. (1984) Zbl0545.49018MR0775682
- ETH-Zürich, Technical Report No. 97/17.
- Nonlinear functional Analysis and Its Applications II/B, Springer, 1983. (1983)

## NotesEmbed ?

topTo embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.