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Funktsional. Anal. i Prilozhen., 2011, Volume 45, Issue 1, Pages 1–15 (Mi faa3031)  

This article is cited in 9 scientific papers (total in 9 papers)

Strongly Elliptic Second-Order Systems with Boundary Conditions on a Nonclosed Lipschitz Surface

M. S. Agranovich

Moscow Institute of Electronics and Mathematics

Abstract: We consider boundary value problems and transmission problems for strongly elliptic second-order systems with boundary conditions on a compact nonclosed Lipschitz surface $S$ with Lipschitz boundary. The main goal is to find conditions for the unique solvability of these problems in the spaces $H^s$, the simplest $L_2$-spaces of the Sobolev type, with the use of potential type operators on $S$. We also discuss, first, the regularity of solutions in somewhat more general Bessel potential spaces and Besov spaces and, second, the spectral properties of problems with spectral parameter in the transmission conditions on $S$, including the asymptotics of the eigenvalues.

Keywords: strong ellipticity, Lipschitz domain, nonclosed boundary, potential type operators, Bessel potential spaces, Besov spaces, regularity of solutions, spectral transmission problems, spectral asymptotics

DOI: https://doi.org/10.4213/faa3031

Full text: PDF file (267 kB)
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English version:
Functional Analysis and Its Applications, 2011, 45:1, 1–12

Bibliographic databases:

UDC: 517.98+517.95
Received: 28.04.2010

Citation: M. S. Agranovich, “Strongly Elliptic Second-Order Systems with Boundary Conditions on a Nonclosed Lipschitz Surface”, Funktsional. Anal. i Prilozhen., 45:1 (2011), 1–15; Funct. Anal. Appl., 45:1 (2011), 1–12

Citation in format AMSBIB
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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. M. S. Agranovich, “Spectral problems in Lipschitz domains”, Journal of Mathematical Sciences, 190:1 (2013), 8–33  mathnet  crossref  mathscinet
    2. M. S. Agranovich, “Mixed Problems in a Lipschitz Domain for Strongly Elliptic Second-Order Systems”, Funct. Anal. Appl., 45:2 (2011), 81–98  mathnet  crossref  crossref  mathscinet  zmath  isi
    3. M. S. Agranovich, A. M. Selitskii, “Fractional Powers of Operators Corresponding to Coercive Problems in Lipschitz Domains”, Funct. Anal. Appl., 47:2 (2013), 83–95  mathnet  crossref  crossref  mathscinet  zmath  isi  elib  elib
    4. Shlapunov A. Tarkhanov N., “On completeness of root functions of Sturm-Liouville problems with discontinuous boundary operators”, J. Differential Equations, 255:10 (2013), 3305–3337  crossref  mathscinet  zmath  adsnasa  isi  elib  scopus
    5. P. Exner, K. Pankrashkin, “Strong coupling asymptotics for a singular Schrödinger operator with an interaction supported by an open arc”, Comm. Partial Differential Equations, 39:2 (2014), 193–212  crossref  mathscinet  zmath  isi  scopus
    6. N. Tarkhanov, A. A. Shlapunov, “Sturm–Liouville problems in weighted spaces in domains with nonsmooth edges. II”, Siberian Adv. Math., 26:4 (2016), 247–293  mathnet  crossref  crossref  mathscinet  elib
    7. Shlapunov A., Peicheva A., “on the Completeness of Root Functions of Sturm-Liouville Problems For the Lame System in Weighted Spaces”, ZAMM-Z. Angew. Math. Mech., 95:11 (2015), 1202–1214  crossref  mathscinet  zmath  isi  elib  scopus
    8. Sybil Yu.M., Grytsko B.E., “Boundary Value Problem For the Two-Dimensional Laplace Equation With Transmission Condition on Thin Inclusion”, J. Numer. Appl. Math., 2:122 (2016), 120–129  isi
    9. Peicheva A.S., “Embedding Theorems For Functional Spaces Associated With a Class of Hermitian Forms”, J. Sib. Fed. Univ.-Math. Phys., 10:1 (2017), 83–95  mathnet  crossref  isi  scopus
  • Функциональный анализ и его приложения Functional Analysis and Its Applications
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