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 Rn, n⩾3. In accordance with the procedure of investigating problems in thin domains, the resulting equation is found on the hyperplane Rn−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.
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”, Russian Acad. Sci. Izv. Math., 44:1 (1995), 91–118
\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 Russian Acad. Sci. Izv. Math.
\yr 1995
\vol 44
\issue 1
\pages 91--118
\mathnet{http://mi.mathnet.ru/eng/im817}
\crossref{https://doi.org/10.1070/IM1995v044n01ABEH001593}
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\zmath{https://zbmath.org/?q=an:0841.35030}
\adsnasa{https://adsabs.harvard.edu/cgi-bin/bib_query?1995IzMat..44...91N}
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Linking options:
https://www.mathnet.ru/eng/im817
https://doi.org/10.1070/IM1995v044n01ABEH001593
https://www.mathnet.ru/eng/im/v58/i1/p92
This publication is cited in the following 4 articles:
Konstantin Pileckas, Alicija Raciene, “Non-stationary Navier–Stokes equations in 2D power cusp domain”, Advances in Nonlinear Analysis, 10:1 (2021), 982
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
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
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
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