Regular Elliptic Boundary-Value Problems in the Extended Sobolev Scale

被引：11

作者：

Anop, A. V. ^{[1
]}

Murach, A. A. ^{[1
]}

机构：

[1] Ukrainian Natl Acad Sci, Inst Math, Kiev, Ukraine

来源：

UKRAINIAN MATHEMATICAL JOURNAL | 2014年 / 66卷 / 07期

关键词：

INTERPOLATION; SPACES;

D O I：

10.1007/s11253-014-0988-6

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We investigate an arbitrary regular elliptic boundary-value problem given in a bounded Euclidean C (a)- domain. It is shown that the operator of the problem is bounded and Fredholm in appropriate pairs of Hormander inner-product spaces. They are parametrized with the help of an arbitrary radial function RO-varying at a and form the extended Sobolev scale. We establish a priori estimates for the solutions of the problem and study their local regularity on this scale. New sufficient conditions for the generalized partial derivatives of the solutions to be continuous are obtained.

引用

页码：969 / 985

页数：17

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