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Funktsional. Anal. i Prilozhen.:

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Funktsional. Anal. i Prilozhen., 2004, Volume 38, Issue 4, Pages 55–72 (Mi faa126)  

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

Elliptic Boundary Value Problems in Hybrid Domains

S. A. Nazarov

Institute of Problems of Mechanical Engineering, Russian Academy of Sciences

Abstract: We derive asymptotic transmission conditions at points where segments are attached to a three-dimensional body. These conditions result in a formally self-adjoint problem on a hybrid set with properties similar to those of standard boundary value problems. In particular, the problem has a zero index and possesses a variational statement. If the systems of differential equations have a special form, then the operator of the problem is realized as a self-adjoint extension of the “decoupled” operators of the problems on the body and the segments. From this viewpoint, we interpret the results of asymptotic analysis of coupled thin and solid bodies.

Keywords: hybrid domain, transmission conditions at points, generalized Green formula, self-adjoint extension


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English version:
Functional Analysis and Its Applications, 2004, 38:4, 283–297

Bibliographic databases:

UDC: 517.923
Received: 18.11.2003

Citation: S. A. Nazarov, “Elliptic Boundary Value Problems in Hybrid Domains”, Funktsional. Anal. i Prilozhen., 38:4 (2004), 55–72; Funct. Anal. Appl., 38:4 (2004), 283–297

Citation in format AMSBIB
\by S.~A.~Nazarov
\paper Elliptic Boundary Value Problems in Hybrid Domains
\jour Funktsional. Anal. i Prilozhen.
\yr 2004
\vol 38
\issue 4
\pages 55--72
\jour Funct. Anal. Appl.
\yr 2004
\vol 38
\issue 4
\pages 283--297

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    This publication is cited in the following articles:
    1. Nazarov S.A., Sokolowski J., “Self-adjoint extensions of differential operators and exterior topological derivatives in shape optimization”, Control Cybernet., 34:3 (2005), 903–925  mathscinet  zmath  isi  elib
    2. S. A. Nazarov, “Korn inequalities for elastic junctions of massive bodies, thin plates, and rods”, Russian Math. Surveys, 63:1 (2008), 35–107  mathnet  crossref  crossref  mathscinet  zmath  isi  elib  elib
    3. Durante T., Kardone D., Nazarov S.A., “Modelirovanie sochlenenii plastin i sterzhnei posredstvom samosopryazhennykh rasshirenii”, Vestn. Sankt-Peterburgskogo un-ta. Ser. 1: Matem., Mekh., Astronom., 2009, no. 2, 3–14
    4. S. A. Nazarov, “Asymptotic behavior of the eigenvalues of the Steklov problem on a junction of domains of different limiting dimensions”, Comput. Math. Math. Phys., 52:11 (2012), 1574–1589  mathnet  crossref  mathscinet  isi  elib  elib
    5. S. A. Nazarov, “Asymptotics of eigen-oscillations of a massive elastic body with a thin baffle”, Izv. Math., 77:1 (2013), 87–142  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    6. Bunoiu R., Cardone G., Nazarov S.A., “Scalar Boundary Value Problems on Junctions of Thin Rods and Plates”, ESAIM-Math. Model. Numer. Anal.-Model. Math. Anal. Numer., 48:5 (2014), 1495–1528  crossref  mathscinet  zmath  isi  scopus
    7. S. A. Nazarov, “Modeling of a Singularly Perturbed Spectral Problem by Means of Self-Adjoint Extensions of the Operators of the Limit Problems”, Funct. Anal. Appl., 49:1 (2015), 25–39  mathnet  crossref  crossref  zmath  isi  elib
    8. V. A. Kozlov, S. A. Nazarov, “Transmission conditions in a one-dimensional model of bifurcating blood vessel with an elastic wall”, J. Math. Sci. (N. Y.), 224:1 (2017), 94–118  mathnet  crossref  mathscinet
    9. Bunoiu R. Cardone G. Nazarov S.A., “Scalar Problems in Junctions of Rods and a Plate II. Self-Adjoint Extensions and Simulation Models”, ESAIM-Math. Model. Numer. Anal.-Model. Math. Anal. Numer., 52:2 (2018), 481–508  crossref  isi
  • Функциональный анализ и его приложения Functional Analysis and Its Applications
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