Elliptic Systems with Almost Regular Coefficients: Singular Weight Integral Operators

2003 ◽  
pp. 25-41
Author(s):  
Stanislav Antontsev
Keyword(s):  
Integral Operators ◽  
Elliptic Systems ◽  
Singular Weight

scholarly journals Singular Integral Operators and Elliptic Boundary-Value Problems. I

2017 ◽  
Vol 63 (1) ◽  
pp. 1-189
Author(s):  
Alexandre P Soldatov
Keyword(s):  
Boundary Value Problems ◽  
Elliptic Boundary ◽  
Boundary Value ◽  
Integral Operators ◽  
Elliptic Systems ◽  
Elliptic Boundary Value Problems ◽  
Main Role ◽  
Cauchy Type ◽  
Elliptic Boundary Value ◽  
First Order

The book consists of three Parts I-III and Part I is presented here. In this book, we develop a new approach mainly based on the author’s papers. Many results are published here for the first time. Chapter 1 is introductory. The necessary background from functional analysis is given there for completeness. In this book, we mostly use weighted Ho¨lder spaces, and they are considered in Ch. 2. Chapter 3 plays the main role: in weighted Ho¨lder spaces we consider there estimates of integral operators with homogeneous difference kernels, which cover potential-type integrals and singular integrals as well as Cauchy-type integrals and double layer potentials. In Ch. 4, analogous estimates are established in weighted Lebesgue spaces. Integrals with homogeneous difference kernels will play an important role in Part III of the monograph, which will be devoted to elliptic boundary-value problems. They naturally arise in integral representations of solutions of first-order elliptic systems in terms of fundamental matrices or their parametrixes. Investigation of boundary-value problems for second-order and higher-order elliptic equations or systems is reduced to first-order elliptic systems.

DEGENERATE ELLIPTIC SYSTEMS OF CLASS I

1987 ◽  
Vol 7 (1) ◽  
pp. 97-108
Author(s):  
Zhibing Deng
Keyword(s):  
Elliptic Systems ◽  
Class I ◽  
Degenerate Elliptic

Multianisotropic integral operators defined by regular equations

2018 ◽  
Vol 60 (3) ◽  
pp. 610-629
Author(s):  
G. A. Karapetyan ◽  
H. A. Petrosyan
Keyword(s):  
Integral Operators
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