The Behavior of Solutions to the Dirichlet Problem for Second Order Elliptic Equations with Variable Nonlinearity Exponent in a Neighborhood of a Conical Boundary Point
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| 024 | 7 | 0 | |a 10.1007/s10958-015-2570-7 |2 doi |
| 035 | |a (NATIONALLICENCE)springer-10.1007/s10958-015-2570-7 | ||
| 245 | 0 | 4 | |a The Behavior of Solutions to the Dirichlet Problem for Second Order Elliptic Equations with Variable Nonlinearity Exponent in a Neighborhood of a Conical Boundary Point |h [Elektronische Daten] |c [Yu. Alkhutov, M. Borsuk] |
| 520 | 3 | |a We study the Dirichlet problem for the p-Laplacian in a conical domain with the homogeneous boundary condition on the lateral surface of a cone with vertex at the origin. We assume that the variable exponent p = p(x) is separated from 1 and ∞ and denote by Ω the intersection of the cone with the unit (n − 1)-dimensional sphere. We prove that (i) if p satisfies the Lipschitz condition and ∂Ω is of class C 2+β, then the solution to the Dirichlet problem is O(|x| λ ) in a neighborhood of the origin, where λ is the sharp exponent of tending to zero of solutions to the same Dirichlet problem for the p(0)-Laplacian and (ii) if p satisfies the Hölder condition, p(0) = 2, and ∂Ω is of class C 1+β, then the solution to the Dirichlet problem is O(|x| λ0) in a neighborhood of the origin, where λ 0 is the sharp exponent of tending to zero of solutions to the same Dirichlet problem for the Laplace operator. Bibliography: 18 titles. | |
| 540 | |a Springer Science+Business Media New York, 2015 | ||
| 700 | 1 | |a Alkhutov |D Yu |u A. G. and N. G. Stoletov Vladimir State University, 87, Gor'kogo St., 600000, Vladimir, Russia |4 aut | |
| 700 | 1 | |a Borsuk |D M. |u University of Warmia and Mazury, 2, Michala Oczapowskiego St., Olsztyn, Poland |4 aut | |
| 773 | 0 | |t Journal of Mathematical Sciences |d Springer US; http://www.springer-ny.com |g 210/4(2015-10-01), 341-370 |x 1072-3374 |q 210:4<341 |1 2015 |2 210 |o 10958 | |
| 856 | 4 | 0 | |u https://doi.org/10.1007/s10958-015-2570-7 |q text/html |z Onlinezugriff via DOI |
| 898 | |a BK010053 |b XK010053 |c XK010000 | ||
| 900 | 7 | |a Metadata rights reserved |b Springer special CC-BY-NC licence |2 nationallicence | |
| 908 | |D 1 |a research-article |2 jats | ||
| 949 | |B NATIONALLICENCE |F NATIONALLICENCE |b NL-springer | ||
| 950 | |B NATIONALLICENCE |P 856 |E 40 |u https://doi.org/10.1007/s10958-015-2570-7 |q text/html |z Onlinezugriff via DOI | ||
| 950 | |B NATIONALLICENCE |P 700 |E 1- |a Alkhutov |D Yu |u A. G. and N. G. Stoletov Vladimir State University, 87, Gor'kogo St., 600000, Vladimir, Russia |4 aut | ||
| 950 | |B NATIONALLICENCE |P 700 |E 1- |a Borsuk |D M. |u University of Warmia and Mazury, 2, Michala Oczapowskiego St., Olsztyn, Poland |4 aut | ||
| 950 | |B NATIONALLICENCE |P 773 |E 0- |t Journal of Mathematical Sciences |d Springer US; http://www.springer-ny.com |g 210/4(2015-10-01), 341-370 |x 1072-3374 |q 210:4<341 |1 2015 |2 210 |o 10958 | ||