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

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

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
\Bibitem{Naz94} \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. \yr 1994 \vol 58 \issue 1 \pages 92--120 \mathnet{http://mi.mathnet.ru/izv817} \mathscinet{http://www.ams.org/mathscinet-getitem?mr=1271516} \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} \isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=A1995QU91700005} 

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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. 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
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
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
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