Abstract:
In this work we study the homogenization for eigenvalues of the fractional p-Laplace operator in a bounded domain both with Dirichlet and Neumann conditions. We obtain the convergence of eigenvalues and the explicit order of the convergence rates when periodic weights are considered. © 2016 Texas State University.
Registro:
Documento: |
Artículo
|
Título: | Eigenvalues homogenization for the fractional p-laplacian |
Autor: | Salort, A.M. |
Filiación: | Departamento de Matemática, FCEN-Universidad de Buenos Aires and IMAS-CON-ICET, Ciudad Universitaria, Pabellón I (1428) Av. Cantilo s/n, Buenos Aires, Argentina
|
Palabras clave: | Eigenvalue homogenization; Fractional p-Laplacian; Nonlinear eigenvalues; Order of convergence |
Año: | 2016
|
Volumen: | 2016
|
Título revista: | Electronic Journal of Differential Equations
|
Título revista abreviado: | Electron. J. Differ. Equ.
|
ISSN: | 10726691
|
Registro: | https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_10726691_v2016_n_p_Salort |
Referencias:
- Bensoussan, A., Lions, J.-L., Papanicolaou, G., Asymptotic Analysis for Periodic Structures, , AMS Chelsea Publishing, Providence, RI, 2011, Corrected reprint of the 1978 original [MR0503330]. MR 2839402
- Blumenthal, R.M., Getoor, R.K., The asymptotic distribution of the eigenvalues for a class of Markov operators (1959) Pacific J. Math, 9, pp. 399-408. , MR 0107298 (21 #6023)
- Boccardo, L., Marcellini, P., Sulla convergenza delle soluzioni di disequazioni variazionali (1976) Ann. Mat. Pura Appl, 110 (4), pp. 137-159. , MR 0425344 (54 #13300)
- Champion, T., De Pascale, L., Asymptotic behaviour of nonlinear eigenvalue problems in-volving p-Laplacian-type operators (2007) Proc. Roy. Soc. Edinburgh Sect. A, 137 (6), pp. 1179-1195. , MR 2376876 (2009b:35315)
- Courant, R., Hilbert, D., (1931) Methoden Der Mathematischen Physik, 1, p. 1937
- Chen, Z.-Q., Song, R., Two-sided eigenvalue estimates for subordinate processes in domains (2005) J. Funct. Anal, 226 (1), pp. 90-113. , MR 2158176 (2006d:60116)
- Del Pezzo, L.M., Salort, A.M., Nonlinear Analysis: Theory (2015) Methods & Applications, 118, pp. 130-143. , The first non-zero Neumann p-fractional eigenvalue
- Demengel, F., Demengel, G., (2012) Functional Spaces for the Theory of Elliptic Partial Differential Equations, , Springer
- Fernandez Bonder, J., Pinasco, J.P., Salort, A.M., Convergence rate for some quasilinear eigenvalues homogenization problems (2015) Journal of Mathematical Analysis and Applications, 423 (2), pp. 1427-1447
- Iannizzotto, A., Squassina, M., Weyl-type laws for fractional p-eigenvalue problems. Asymp-tot (2014) Anal, 88 (4), pp. 233-245
- Kenig, C., Lin, F., Shen, Z., Estimates of eigenvalues and eigenfunctions in periodic homoge-nization (2013) J. Eur. Math. Soc, 15 (5), pp. 1901-1925. , MR 3082248
- Kesavan, S., Homogenization of elliptic eigenvalue problems. II (1979) Appl. Math. Optim, 5 (3), pp. 197-216. , MR 546068 (80i:65110)
- Kenig, C., Lin, F., Shen, Z., Convergence rates in L2 for elliptic homogenization problems (2012) Arch. Ration. Mech. Anal, 203 (3), pp. 1009-1036. , MR 2928140
- Lindqvist, P., On the equation div (Formula presented) (1990) Proc. Amer. Math. Soc, 109 (1), pp. 157-164
- Motreanu, D., Motreanu, V.V., Papageorgiou, N.S., (2014) Topological and Variational Methods with Applications to Nonlinear Boundary Value Problems, pp. 11+459. , Springer, New York
- Oleĭnik, O.A., Shamaev, A.S., Yosifian, G.A., Mathematical problems in elasticity and homog-enization Studies in Mathematics and Its Applications, 26. , North-Holland Publishing Co., Amsterdam, 1992. MR 1195131 (93k:35025)
- Sánchez-Palencia, E., Équations aux dérivées partielles dans un type de milieux hétérogénes C. R. Acad. Sci. Paris Sér, , A-B
- Schneider, C., (2008) Trace Operators in Besov and Triebel-Lizorkin Spaces, , Univ. Leipzig, Fak. fur Mathematik U. Informatik
- Servadei, R., Valdinoci, E., Variational methods for non-local operators of elliptic type (2013) Discrete Contin. Dyn. Syst, 33 (5), pp. 2105-2137
Citas:
---------- APA ----------
(2016)
. Eigenvalues homogenization for the fractional p-laplacian. Electronic Journal of Differential Equations, 2016.
Recuperado de https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_10726691_v2016_n_p_Salort [ ]
---------- CHICAGO ----------
Salort, A.M.
"Eigenvalues homogenization for the fractional p-laplacian"
. Electronic Journal of Differential Equations 2016
(2016).
Recuperado de https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_10726691_v2016_n_p_Salort [ ]
---------- MLA ----------
Salort, A.M.
"Eigenvalues homogenization for the fractional p-laplacian"
. Electronic Journal of Differential Equations, vol. 2016, 2016.
Recuperado de https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_10726691_v2016_n_p_Salort [ ]
---------- VANCOUVER ----------
Salort, A.M. Eigenvalues homogenization for the fractional p-laplacian. Electron. J. Differ. Equ. 2016;2016.
Available from: https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_10726691_v2016_n_p_Salort [ ]