Abstract:
Upper bounds are obtained for solutions of the Dirichlet problem for pseudodifferential elliptic equations where the right-hand side has compact support. In domains with non-compact boundary they characterise the behaviour of solutions at infinity in its dependence on the geometric properties of the domain. For unbounded domains where the boundary has irregular behaviour, it is shown that these bounds may be more efficient than the bounds that are already known for second-order elliptic equations. For second-order elliptic equations
in a broad class of domains of revolution these bounds are shown to be sharp.
Bibliography: 17 titles.
Citation:
L. M. Kozhevnikova, “Behaviour at infinity of solutions of pseudodifferential
elliptic equations in unbounded domains”, Sb. Math., 199:8 (2008), 1169–1200
\Bibitem{Koz08}
\by L.~M.~Kozhevnikova
\paper Behaviour at infinity of solutions of pseudodifferential
elliptic equations in unbounded domains
\jour Sb. Math.
\yr 2008
\vol 199
\issue 8
\pages 1169--1200
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Linking options:
https://www.mathnet.ru/eng/sm4235
https://doi.org/10.1070/SM2008v199n08ABEH003958
https://www.mathnet.ru/eng/sm/v199/i8/p61
This publication is cited in the following 6 articles:
L. M. Kozhevnikova, A. A. Khadzhi, “O resheniyakh ellipticheskikh uravnenii s nestepennymi nelineinostyami v neogranichennykh oblastyakh”, Vestn. Sam. gos. tekhn. un-ta. Ser. Fiz.-mat. nauki, 19:1 (2015), 44–62
L. M. Kozhevnikova, A. A. Khadzhi, “Resheniya anizotopnykh ellipticheskikh uravnenii v neogranichennykh oblastyakh”, Vestn. Sam. gos. tekhn. un-ta. Ser. Fiz.-mat. nauki, 1(30) (2013), 90–96
L. M. Kozhevnikova, “Stabilization of solutions of pseudo-differential parabolic equations in unbounded domains”, Izv. Math., 74:2 (2010), 325–345
R. Kh. Karimov, L. M. Kozhevnikova, “Stabilization of solutions of quasilinear second order parabolic equations in domains with non-compact boundaries”, Sb. Math., 201:9 (2010), 1249–1271
R. Kh. Karimov, L. M. Kozhevnikova, “Povedenie na beskonechnosti reshenii kvazilineinykh ellipticheskikh uravnenii vtorogo poryadka v neogranichennykh oblastyakh”, Ufimsk. matem. zhurn., 2:2 (2010), 53–66
L. M. Kozhevnikova, “O suschestvovanii i edinstvennosti reshenii zadachi Dirikhle dlya psevdodifferentsialnykh ellipticheskikh uravnenii v oblastyakh s nekompaktnymi granitsami”, Ufimsk. matem. zhurn., 1:1 (2009), 38–68
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