MULTILAYER POTENTIALS FOR HIGHER-ORDER SYSTEMS IN ROUGH DOMAINS

被引：0

作者：

Hoepfner, Gustavo ^{[1
]}

Liboni, Paulo ^{[2
]}

Mitrea, Dorina ^{[3
]}

Mitrea, Irina ^{[4
]}

Mitrea, Marius ^{[3
]}

机构：

[1] Univ Fed Sao Carlos, Dept Matemat, Sao Carlos, Brazil

[2] Univ Estadual Londrina, Dept Matemat, Londrina, Parana, Brazil

[3] Baylor Univ, Dept Math, Waco, TX 76798 USA

[4] Temple Univ, Dept Math, Philadelphia, PA 19122 USA

来源：

ANALYSIS & PDE | 2021年 / 14卷 / 04期

基金：

欧洲研究理事会; 美国国家科学基金会; 巴西圣保罗研究基金会;

关键词：

higher-order system; multilayer operator; boundary layer potential; Calderon-Zygmund operator; principal value singular integral operator; set of locally finite perimeter; Ahlfors regular set; uniformly rectifiable set; divergence theorem; nontangential maximal operators; nontangential boundary trace; Whitney arrays; boundary Sobolev space; Carleson measure; Dirichlet boundary problem; regularity boundary problem; DIRICHLET PROBLEM; LAYER POTENTIALS; NEUMANN PROBLEM; EQUATION;

D O I：

10.2140/apde.2021.14.1233

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We initiate the study of multilayer potential operators associated with any given homogeneous constant-coefficient higher-order elliptic system L in an open set Omega subset of R-n satisfying additional assumptions of a geometric measure theoretic nature. We develop a Calderon-Zygmund-type theory for this brand of singular integral operators acting on Whitney arrays, starting with the case when Omega is merely of locally finite perimeter and then progressively strengthening the hypotheses by ultimately assuming that Omega is a uniformly rectifiable domain (which is the optimal setting where singular integral operators of principal value type are known to be bounded on Lebesgue spaces), and conclude by indicating how this body of results is significant in the context of boundary value problems for the higher-order system L in such a domain Omega.

引用

页码：1233 / 1308

页数：76

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