The Dirichlet-to-Neumann operator on rough domains

被引：52

作者：

Arendt, W. ^{[2
]}

ter Elst, A. F. M. ^{[1
]}

机构：

[1] Univ Auckland, Dept Math, Auckland 1142, New Zealand

[2] Univ Ulm, Inst Appl Anal, D-89081 Ulm, Germany

来源：

JOURNAL OF DIFFERENTIAL EQUATIONS | 2011年 / 251卷 / 08期

关键词：

Dirichlet-to-Neumann operator; Trace; Form methods; Rough boundary; Irreducible semigroup; ROBIN BOUNDARY-CONDITIONS; ARBITRARY DOMAINS; LAPLACIAN;

D O I：

10.1016/j.jde.2011.06.017

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We consider a bounded connected open set Omega subset of R-d whose boundary Gamma has a finite (d - 1)-dimensional Hausdorff measure. Then we define the Dirichlet-to-Neumann operator D-0 on L-2(Gamma) by form methods. The operator -D-0 is self-adjoint and generates a contractive C-0-semigroup S = (S-t)(t > 0) on L-2(Gamma). We show that the asymptotic behaviour of S-t as t -> infinity is related to properties of the trace of functions in H-1(Omega) which Omega may or may not have. (C) 2011 Elsevier Inc. All rights reserved.

引用

页码：2100 / 2124

页数：25

共 21 条

[1]

[Anonymous], 1996, Applied Mathematical Sciences

[2]

[Anonymous], 2000, Oxford Mathematical Monographs

[3]

[Anonymous], 1992, Measure theory and fine properties of functions

[4]

[Anonymous], 1991, DEGRUYTER STUD MATH

[5]

[Anonymous], 1985, LINEARE FUNKTIONALAN

[6]

[Anonymous], 1994, DIRICHLET FORMS SYMM

[7]

[Anonymous], 1989, CAMBRIDGE TRACTS MAT

[8] The Laplacian with Wentzell-Robin boundary conditions on spaces of continuous functions [J].

Arendt, W ;

Metafune, G ;

Pallara, D ;

Romanelli, S .

SEMIGROUP FORUM, 2003, 67 (02) :247-261

[9] The Laplacian with Robin boundary conditions on arbitrary domains [J].

Arendt, W ;

Warma, M .

POTENTIAL ANALYSIS, 2003, 19 (04) :341-363

[10]

ARENDT W, 2011, J OPERATOR IN PRESS

← 1 2 3 →