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Funktsional. Anal. i Prilozhen., 2011, Volume 45, Issue 2, Pages 1–22 (Mi faa3039)  

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

Mixed Problems in a Lipschitz Domain for Strongly Elliptic Second-Order Systems

M. S. Agranovich

Moscow Institute of Electronics and Mathematics

Abstract: We consider mixed problems for strongly elliptic second-order systems in a bounded domain with Lipschitz boundary in the space $\mathbb{R}^n$. For such problems, equivalent equations on the boundary in the simplest $L_2$-spaces $H^s$ of Sobolev type are derived, which permits one to represent the solutions via surface potentials. We prove a result on the regularity of solutions in the slightly more general spaces $H^s_p$ of Bessel potentials and Besov spaces $B^s_p$. Problems with spectral parameter in the system or in the condition on a part of the boundary are considered, and the spectral properties of the corresponding operators, including the eigenvalue asymptotics, are discussed.

Keywords: strongly elliptic system, mixed problem, potential type operator, spectral problem, eigenvalue asymptotics

DOI: https://doi.org/10.4213/faa3039

Full text: PDF file (333 kB)
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English version:
Functional Analysis and Its Applications, 2011, 45:2, 81–98

Bibliographic databases:

UDC: 517.98+517.95
Received: 16.12.2010

Citation: M. S. Agranovich, “Mixed Problems in a Lipschitz Domain for Strongly Elliptic Second-Order Systems”, Funktsional. Anal. i Prilozhen., 45:2 (2011), 1–22; Funct. Anal. Appl., 45:2 (2011), 81–98

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, “Strongly Elliptic Second-Order Systems with Boundary Conditions on a Nonclosed Lipschitz Surface”, Funct. Anal. Appl., 45:1 (2011), 1–12  mathnet  crossref  crossref  mathscinet  zmath  isi
    2. Agranovich M.S., “Remarks on strongly elliptic systems in Lipschitz domains”, Russ. J. Math. Phys., 19:4 (2012), 405–416  crossref  mathscinet  zmath  isi  elib  scopus
    3. Alexander N. Polkovnikov, Aleksander A. Shlapunov, “On the spectral properties of a non-coercive mixed problem associated with $\overline\partial$-operator”, Zhurn. SFU. Ser. Matem. i fiz., 6:2 (2013), 247–261  mathnet
    4. 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
    5. Shlapunov A. Tarkhanov N., “On Completeness of Root Functions of Sturm-Liouville Problems with Discontinuous Boundary Operators”, J. Differ. Equ., 255:10 (2013), 3305–3337  crossref  mathscinet  zmath  adsnasa  isi  elib  scopus
    6. N. D. Kopachevsky, “Abstract Green formulas for triples of Hilbert spaces and sesquilinear forms”, Journal of Mathematical Sciences, 225:2 (2017), 226–264  mathnet  crossref
    7. 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
    8. Gurevich P. Vaeth M., “Stability for Semilinear Parabolic Problems in $L_2$ and $W^{1,2}$”, Z. Anal. ihre. Anwend., 35:3 (2016), 333–357  crossref  mathscinet  zmath  isi  elib  scopus
    9. Lotoreichik V., Rohleder J., “Eigenvalue Inequalities For the Laplacian With Mixed Boundary Conditions”, J. Differ. Equ., 263:1 (2017), 491–508  crossref  mathscinet  zmath  isi  scopus
  • Функциональный анализ и его приложения Functional Analysis and Its Applications
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