STABILITY RESULTS FOR THE ROBIN-LAPLACIAN ON NONSMOOTH DOMAINS

被引：1

作者：

Bucur, Dorin ^{[1
]}

Giacomini, Alessandro ^{[2
]}

Trebeschi, Paola ^{[2
]}

机构：

[1] Univ Savoie Mt Blanc, LAMA, CNRS, Campus Sci, F-73376 Le Bourget Du Lac, France

[2] Univ Brescia, Sez Matemat, DICATAM, I-25123 Brescia, Italy

来源：

SIAM JOURNAL ON MATHEMATICAL ANALYSIS | 2022年 / 54卷 / 04期

关键词：

Robin-Laplacian; rectifiable sets; functions of bounded variation; lower semicontinuity; Hausdorff convergence; BOUNDARY-CONDITIONS; ELLIPTIC PROBLEMS;

D O I：

10.1137/22M1471250

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We formulate a generalization of the Laplace equation under Robin boundary conditions on a large class of possibly nonsmooth domains by dealing with the trace term appearing in the variational formulation from the point of view of the theory of functions of bounded variation. Admissible domains may have inner boundaries, i.e., inner cracks. In dimension two, we formulate a stability result for the elliptic problems under domain variation: with this aim, we introduce a notion of perimeter (Robin perimeter) which is tailored to count the inner boundaries with the appropriate natural multiplicity.

引用

页码：4591 / 4624

页数：34

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