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Izv. RAN. Ser. Mat., 2003, Volume 67, Issue 5, Pages 49–82 (Mi izv451)  

This article is cited in 7 scientific papers (total in 7 papers)

On solutions of mixed boundary-value problems for the elasticity system in unbounded domains

H. Matevossian

Steklov Mathematical Institute, Russian Academy of Sciences

Abstract: We study the properties of generalized solutions of mixed boundary-value problems for the linear system of elasticity theory in the exterior of a compact set and in a half-space under the assumption that the energy integral with weight $|x|^a$ is finite for such solutions. Depending on the value of the parameter $a$, a uniqueness criterion is established for these solutions, and exact formulae are obtained for the dimension of the space of solutions.

DOI: https://doi.org/10.4213/im451

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English version:
Izvestiya: Mathematics, 2003, 67:5, 895–929

Bibliographic databases:

UDC: 517.95
MSC: 35Q72, 35J55, 74G30, 74G35
Received: 12.11.2002

Citation: H. Matevossian, “On solutions of mixed boundary-value problems for the elasticity system in unbounded domains”, Izv. RAN. Ser. Mat., 67:5 (2003), 49–82; Izv. Math., 67:5 (2003), 895–929

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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. O. A. Matevosyan, “Solutions of the Robin problem for the system of elastic theory in external domains”, J. Math. Sci. (N. Y.), 197:3 (2014), 367–394  mathnet  crossref  elib
    2. Matevosyan O.A., “Solution of a Mixed Boundary Value Problem For the Biharmonic Equation With Finite Weighted Dirichlet Integral”, Differ. Equ., 51:4 (2015), 487–501  mathnet  crossref  mathscinet  zmath  isi  elib  scopus
    3. Matevosyan O.A., “On solutions of the mixed Dirichlet–Navier problem for the polyharmonic equation in exterior domains”, Russ. J. Math. Phys., 23:1 (2016), 135–138  crossref  mathscinet  zmath  isi  elib  scopus
    4. H. A. Matevossian, “Mixed Dirichlet–Steklov problem for the biharmonic equation in weighted spaces”, J. Math. Sci. (N. Y.), 234:4 (2018), 440–454  mathnet  crossref
    5. Matevossian H.A., “On the biharmonic Steklov problem in weighted spaces”, Russ. J. Math. Phys., 24:1 (2017), 134–138  crossref  mathscinet  zmath  isi  scopus
    6. Matevossian H.A., “On Solutions of the Mixed Dirichlet-Steklov Problem For the Biharmonic Equation in Exterior Domains”, P-Adic Numbers Ultrametric Anal. Appl., 9:2 (2017), 151–157  crossref  mathscinet  zmath  isi  scopus
    7. Matevossian H.A., “On the Steklov-Type Biharmonic Problem in Unbounded Domains”, Russ. J. Math. Phys., 25:2 (2018), 271–276  crossref  mathscinet  isi  scopus
  • Известия Российской академии наук. Серия математическая Izvestiya: Mathematics
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