THE DIRICHLET PROBLEM IN LIPSCHITZ DOMAINS FOR HIGHER ORDER ELLIPTIC SYSTEMS WITH ROUGH COEFFICIENTS

被引：48

作者：

Maz'ya, V. ^{[1
,2
,3
]}

Mitrea, M. ^{[4
]}

Shaposhnikova, T. ^{[1
,3
]}

机构：

[1] Ohio State Univ, Dept Math, Columbus, OH 43210 USA

[2] Univ Liverpool, Dept Math Sci, Liverpool L69 3BX, Merseyside, England

[3] Linkoping Univ, Dept Math, SE-58183 Linkoping, Sweden

[4] Univ Missouri, Dept Math, Columbia, MO 65211 USA

来源：

JOURNAL D ANALYSE MATHEMATIQUE | 2010年 / 110卷

关键词：

VMO COEFFICIENTS; LAYER POTENTIALS; DIVERGENCE FORM; NEUMANN PROBLEM; SOBOLEV SPACES; HARDY-SPACES; EQUATIONS; BOUNDARY; SOLVABILITY; VARIABLES;

D O I：

10.1007/s11854-010-0005-4

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We study the Dirichlet problem, in Lipschitz domains and with boundary data in Besov spaces, for divergence form strongly elliptic systems of arbitrary order with bounded, complex-valued coefficients. A sharp corollary of our main solvability result is that the operator of this problem performs an isomorphism between weighted Sobolev spaces when its coefficients and the unit normal of the boundary belong to the space VMO.

引用

页码：167 / 239

页数：73

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