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Izv. RAN. Ser. Mat., 1994, Volume 58, Issue 1, Pages 92–120 (Mi izv817)  

This article is cited in 3 scientific papers (total in 3 papers)

Asymptotic of a solution of the Neumann problem at a point of tangency of smooth components of the boundary of the domain

S. A. Nazarov


Abstract: The asymptotics of the solution of the Neumann problem is studied for a second-order elliptic equation near a point of tangency of two surfaces forming the boundary of a domain in $\mathbf R^n$, $n\geqslant 3$. In accordance with the procedure of investigating problems in thin domains, the resulting equation is found on the hyperplane $\mathbf R^{n-1}$, the power solutions of which occur in the asymptotics. The justification of the expansion first found formally is based on a priori estimates of solutions in spaces with weighted norms, reduction of the problem to the resulting equation by means of integration, and application of a familiar theorem regarding the asymptotics of the latter.

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English version:
Russian Academy of Sciences. Izvestiya Mathematics, 1995, 44:1, 91–118

Bibliographic databases:

UDC: 517.946
MSC: 35J25, 35B40
Received: 15.12.1992

Citation: S. A. Nazarov, “Asymptotic of a solution of the Neumann problem at a point of tangency of smooth components of the boundary of the domain”, Izv. RAN. Ser. Mat., 58:1 (1994), 92–120; Russian Acad. Sci. Izv. Math., 44:1 (1995), 91–118

Citation in format AMSBIB
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\by S.~A.~Nazarov
\paper Asymptotic of a solution of the Neumann problem at a point of tangency of smooth components of the boundary of the domain
\jour Izv. RAN. Ser. Mat.
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\vol 58
\issue 1
\pages 92--120
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\zmath{https://zbmath.org/?q=an:0841.35030}
\adsnasa{http://adsabs.harvard.edu/cgi-bin/bib_query?1995IzMat..44...91N}
\transl
\jour Russian Acad. Sci. Izv. Math.
\yr 1995
\vol 44
\issue 1
\pages 91--118
\crossref{https://doi.org/10.1070/IM1995v044n01ABEH001593}
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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. Nazarov S.A. Sokolowski J. Taskinen J., “Neumann Laplacian on a Domain with Tangential Components in the Boundary”, Ann. Acad. Sci. Fenn. Ser. A1-Math., 34:1 (2009), 131–143  mathscinet  zmath  isi
    2. Nazarov S.A. Taskinen J., “Spectral Anomalies of the Robin Laplacian in Non-Lipschitz Domains”, J. Math. Sci.-Univ. Tokyo, 20:1 (2013), 27–90  isi
    3. Munnier A., Ramdani K., “Asymptotic Analysis of a Neumann Problem in a Domain with Cusp. Application to the Collision Problem of Rigid Bodies in a Perfect Fluid”, SIAM J. Math. Anal., 47:6 (2015), 4360–4403  crossref  mathscinet  zmath  isi  elib  scopus
  • Известия Российской академии наук. Серия математическая Izvestiya: Mathematics
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