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Matematicheskie Trudy, 2015, Volume 18, Number 2, Pages 133–204
DOI: https://doi.org/10.17377/mattrudy.2015.18.208
(Mi mt297)
 

This article is cited in 3 scientific papers (total in 3 papers)

Sturm–Liouville problems in weighted spaces in domains with nonsmooth edges. II

N. Tarkhanova, A. A. Shlapunovb

a Universität Potsdam, Institut für Mathematik, Am Neuen Palais, 10, Potsdam, 14469 GERMANY
b Institute of Mathematics and Computer Science, Siberian Federal University, Krasnoyarsk
Full-text PDF (582 kB) Citations (3)
References:
Abstract: We consider a (generally, noncoercive) mixed boundary value problem in a bounded domain $\mathcal{D}$ of ${\mathbb{R}}^n$ for a second order elliptic differential operator $A (x,\partial)$. The differential operator is assumed to be of divergent form in $\mathcal{D}$ and the boundary operator $B (x,\partial)$ is of Robin type on $\partial \mathcal{D}$. The boundary of $\mathcal{D}$ is assumed to be a Lipschitz surface. Besides, we distinguish a closed subset $Y \subset \partial \mathcal{D}$ and control the growth of solutions near $Y$. We prove that the pair $(A,B)$ induces a Fredholm operator $L$ in suitable weighted spaces of Sobolev type, the weight function being a power of the distance to the singular set $Y$. Moreover, we prove the completeness of root functions related to $L$.
Key words: mixed problems, noncoercive boundary conditions, elliptic operators, root functions, weighted Sobolev spaces.
Received: 01.04.2014
English version:
Siberian Advances in Mathematics, 2016, Volume 26, Issue 4, Pages 247–293
DOI: https://doi.org/10.3103/S1055134416040027
Bibliographic databases:
Document Type: Article
UDC: 517.95+517.98
Language: Russian
Citation: N. Tarkhanov, A. A. Shlapunov, “Sturm–Liouville problems in weighted spaces in domains with nonsmooth edges. II”, Mat. Tr., 18:2 (2015), 133–204; Siberian Adv. Math., 26:4 (2016), 247–293
Citation in format AMSBIB
\Bibitem{TarShl15}
\by N.~Tarkhanov, A.~A.~Shlapunov
\paper Sturm--Liouville problems in weighted spaces in domains with nonsmooth edges.~II
\jour Mat. Tr.
\yr 2015
\vol 18
\issue 2
\pages 133--204
\mathnet{http://mi.mathnet.ru/mt297}
\crossref{https://doi.org/10.17377/mattrudy.2015.18.208}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=3588295}
\elib{https://elibrary.ru/item.asp?id=24639787}
\transl
\jour Siberian Adv. Math.
\yr 2016
\vol 26
\issue 4
\pages 247--293
\crossref{https://doi.org/10.3103/S1055134416040027}
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