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Mat. Zametki, 2000, Volume 68, Issue 6, Pages 874–886 (Mi mz1011)  

This article is cited in 6 scientific papers (total in 6 papers)

Weak Solvability of the Dirichlet Problem on Stratified Sets

O. M. Penkin, E. M. Bogatov

Voronezh State University

Abstract: The Dirichlet problem is posed for an analog of the Beltrami–Laplace operator on sets consisting of manifolds of various dimensions regularly adjacent to one another (stratified sets). A special system of notions permits one to prove analogs of Green's integral identities and the Poincaré inequality for Sobolev type spaces. The weak solvability of the Dirichlet problem for this operator, as well as for an analog of the biharmonic operator, is proved on the basis of the Riesz theorem on the representation of linear functionals.

DOI: https://doi.org/10.4213/mzm1011

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English version:
Mathematical Notes, 2000, 68:6, 740–750

Bibliographic databases:

UDC: 517.956.2
Received: 02.11.1998
Revised: 01.02.2000

Citation: O. M. Penkin, E. M. Bogatov, “Weak Solvability of the Dirichlet Problem on Stratified Sets”, Mat. Zametki, 68:6 (2000), 874–886; Math. Notes, 68:6 (2000), 740–750

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. E. M. Bogatov, O. M. Penkin, “The Fourier method in the Cauchy problem for a fourth-order equation on stratified sets”, Russian Math. (Iz. VUZ), 47:8 (2003), 65–69  mathnet  mathscinet  zmath  elib
    2. Bogatov, EM, “On the solvability of hyperbolic equations and elliptic inequalities on stratified sets”, Differential Equations, 39:12 (2003), 1794  mathnet  crossref  mathscinet  zmath  isi  scopus
    3. E. M. Bogatov, “Approximation of the eigenfrequencies of a triangular grid of bars”, Comput. Math. Math. Phys., 45:8 (2005), 1350–1357  mathnet  mathscinet  zmath
    4. L. A. Kovaleva, “O modifitsirovannoi zadache Bitsadze–Samarskogo”, Vestn. Sam. gos. tekhn. un-ta. Ser. Fiz.-mat. nauki, 1(14) (2007), 10–15  mathnet  crossref
    5. S. L. Semenov, “Razreshimost v klassicheskom smysle zadachi Puassona dlya operatora Laplasa na dvumernykh stratifitsirovannykh mnozhestvakh”, Izv. Sarat. un-ta. Nov. ser. Ser. Matematika. Mekhanika. Informatika, 12:1 (2012), 38–52  mathnet  crossref  elib
    6. R. Ch. Kulaev, “O funktsii Grina parabolicheskoi zadachi na grafe”, Vladikavk. matem. zhurn., 14:4 (2012), 32–40  mathnet
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