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

[11]

Arendt W., 1986, Lecture Notes in Math., V1184

[12]

Arendt W., 2007, Ulmer Seminare, V12, P23

[13] A Variational Approach to the Isoperimetric Inequality for the Robin Eigenvalue Problem [J].

Bucur, Dorin ;

Giacomini, Alessandro .

ARCHIVE FOR RATIONAL MECHANICS AND ANALYSIS, 2010, 198 (03) :927-961

[14] Robin boundary value problems on arbitrary domains [J].

Daners, D .

TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, 2000, 352 (09) :4207-4236

[15]

EDMUNDS D. E., 1987, OXFORD MATH MONOGR

[16]

Engel KJ, 2003, ARCH MATH, V81, P548, DOI 10.1007/s00013-003-0557-y

[17]

Escher J., 1994, ANN SCUOLA NORM SUP, V21, P235

[18]

Fremlin D. H., 2003, MEASURE THEORY, VTwo

[19]

Gilbarg D., 1983, ELLIPTIC PARTIAL DIF, V2nd

[20]

Mazja V., 1985, SPRINGER SER SOV MAT

← 1 2 3 →