Abstract:
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 Hölder spaces, and they are considered in
Ch. 2. Chapter 3 plays the main role: in weighted
Hölder 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.
Bibliographic databases:
Document Type:
Article
UDC:517.968
Language: Russian
Citation:
A. P. Soldatov, “Singular integral operators and elliptic boundary-value problems. I”, Functional analysis, CMFD, 63, no. 1, Peoples' Friendship University of Russia, M., 2017, 1–189
\Bibitem{Sol17}
\by A.~P.~Soldatov
\paper Singular integral operators and elliptic boundary-value problems.~I
\inbook Functional analysis
\serial CMFD
\yr 2017
\vol 63
\issue 1
\pages 1--189
\publ Peoples' Friendship University of Russia
\publaddr M.
\mathnet{http://mi.mathnet.ru/cmfd316}
\crossref{https://doi.org/10.22363/2413-3639-2017-63-1-1-189}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=3646636}
Linking options:
https://www.mathnet.ru/eng/cmfd316
https://www.mathnet.ru/eng/cmfd/v63/i1/p1
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