ELLIPTIC BOUNDARY-VALUE PROBLEMS IN HORMANDER SPACES

被引:0
作者
Anop, Anna [1 ,2 ]
Kasirenko, Tetiana [1 ]
机构
[1] Natl Acad Sci Ukraine, Inst Math, 3 Tereshchenkivska, UA-01601 Kiev, Ukraine
[2] Chernihiv Natl Pedag Univ, 53 Hetmana Polubotka, UA-14013 Chernihiv, Ukraine
来源
METHODS OF FUNCTIONAL ANALYSIS AND TOPOLOGY | 2016年 / 22卷 / 04期
关键词
Elliptic problem; Hormander space; extended Sobolev scale; RO-varying function; Fredholm property; a priori estimate; local regularity;
D O I
暂无
中图分类号
O1 [数学];
学科分类号
0701 ; 070101 ;
摘要
We investigate general elliptic boundary-value problems in Hormander inner product spaces that form the extended Sobolev scale. The latter consists of all Hilbert spaces that are interpolation spaces with respect to the Sobolev Hilbert scale. We prove that the operator corresponding to an arbitrary elliptic problem is Fredholm in appropriate couples of the Hormander spaces and induces a collection of isomorphisms on the extended Sobolev scale. We obtain a local a priory estimate for generalized solutions to this problem and prove a theorem on their local regularity in the Hormander spaces. We find new sufficient conditions under which generalized derivatives (of a given order) of the solutions are continuous.
引用
收藏
页码:295 / 310
页数:16
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