Artículo

Estamos trabajando para incorporar este artículo al repositorio
Consulte el artículo en la página del editor
Consulte la política de Acceso Abierto del editor

Abstract:

We find an interpretation using optimal mass transport theory for eigenvalue problems obtained as limits of the eigenvalue problems for the fractional p-Laplacian operators as p → +∞. We deal both with Dirichlet and Neumann boundary conditions. © 2015 by De Gruyter.

Registro:

Documento: Artículo
Título:An optimal mass transport approach for limits of eigenvalue problems for the fractional p-Laplacian
Autor:Del Pezzo, L.; Rossi, J.; Saintier, N.; Salort, A.
Filiación:Departamento de Matemática, Facultad de Ciencias Exactas y Naturales, Universidad de Buenos Aires, Pabellón 1, Buenos Aires, 1428, Argentina
Instituto de Ciencias, Universidad Nacional de General Sarmiento, Juan María Gutierrez 1150, Los Polvorines, Provincia de Buenos Aires, C. P. 1613, Argentina
Palabras clave:eigenvalues; Fractional p-Laplacian; mass transport
Año:2015
Volumen:4
Número:3
Página de inicio:235
Página de fin:249
DOI: http://dx.doi.org/10.1515/anona-2015-0013
Título revista:Advances in Nonlinear Analysis
Título revista abreviado:Adv. Nonlinear Anal.
ISSN:21919496
Registro:https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_21919496_v4_n3_p235_DelPezzo

Referencias:

  • Aronsson, G., Extension of functions satisfying Lipschitz conditions (1967) Ark. Mat., 6, pp. 551-561
  • Aronsson, G., Crandalland, P., Juutinen, M.G., A tour of the theory of absolutely minimizing functions (2004) Bull. Amer. Math. Soc. (N.S.), 41 (4), pp. 439-505
  • Belloni, M., Kawohl, B., The pseudo-p-Laplace eigenvalue problem and viscosity solutions as p → oo (2004) ESAIM Control Optim. Calc. Var., 10, pp. 28-52
  • Bhattacharya, T., Di Benedetto, E., Manfredi, J., Limits asp oo of h<inf>p</inf>u<inf>p</inf> = f and related extremal problems (1989) Rend. Semin. Mat. Univ. Politec. Torino, 47, pp. 15-18. , special issue
  • Champion, T., De Pascale, L., Jimenez, C., The oo-eigenvalue problem and a problem of optimal transportation (2009) Commun. Appl.Anal., 13 (4), pp. 547-565
  • Crandall, M.G., Ishii, H., Lions, P.L., User's guide to viscosity solutions of second order partial differential equations (1992) Bull. Amer. Math. Soc. (N.S.), 27 (1), pp. 1-67
  • Dal Maso, G., An Introduction to G-Convergence (1993) Progr. Nonlinear Differential Equations Appl., 8. , Birkhäuser, Boston
  • Del Pezzo, L.M., Salort, A.M., The first non-zero Neumann p-fractional eigenvalue (2015) Nonlinear Anal., 118, pp. 130-143
  • Demengel, F., Demengel, G., (2012) Functional Spaces for the Theory of Elliptic Partial Differential Equations, , Universitext, Springer, London
  • Dipierro, S., Ros-Oton, X., Valdinoci, E., (2014) Nonlocal Problems with Neumann Boundary Conditions, , http://arxiv.org/absl407.3313, preprint
  • Di Nezza, E., Palatucci, G., Valdinoci, E., Hitchhiker's guide to the fractional Sobolev spaces (2012) Bull. Sci. Math., 136 (5), pp. 521-573
  • Esposito, L., Kawohl, B., Nitsch, C., Trombetti, C., The Neumann eigenvalue problem fortheoo-Laplacian Atti Accad. Naz. Lincei Cl. Sci. Fis. Mat. Natur. Rend. Lincei (9) Mat. Appl, , to appear
  • Garcia-Azorero, J., Manfredi, J.J., Peral, I., Rossi, J.D., Steklov eigenvalues for the oo-Laplacian, AttiAccad (2006) Naz. Lincei Cl. Sci. Fis. Mat. Natur. Rend. Lincei (9) Mat. Appl., 17 (3), pp. 199-210
  • Jensen, R., Uniqueness of Lipschitz extensions: Minimizing the sup norm of the gradient (1993) Arch. Ration. Mech.Anal., 123 (1), pp. 51-74
  • Juutinen, P., Lindqvist, P., On the higher eigenvalues fortheoo-eigenvalue problem (2005) Calc. Var. Partial Differential Equations, 23 (2), pp. 169-192
  • Juutinen, P., Lindqvist, P., Manfredi, J.J., Theoo-eigenvalue problem (1999) Arch. Ration. Mech.Anal., 148 (2), pp. 89-105
  • Jylha, H., An optimal transportation problem related to the limits of solutions of local and nonlocalp-Laplace-type problems (2015) Rev. Mat. Complut., 28 (1), pp. 85-121
  • Lê, A., On the first eigenvalue of the Steklov eigenvalue problem for the infinity Laplacian (2006) Electron. J. Differential Equations, 111, pp. 1-9
  • Lindgren, E., Lindqvist, P., Fractional eigenvalues (2014) Calc. Var. Partial Differential Equations, 49 (1-2), pp. 795-826
  • Molica Bisci, G., Sequence of weak solutions for fractional equations (2014) Math. Res. Lett., 21 (2), pp. 241-253
  • Molica Bisci, G., Fractional equations with bounded primitive (2014) Appl. Math. Lett., 27, pp. 53-58
  • Molica Bisci, G., Pansera, B.A., Three weak solutions for nonlocal fractional equations (2014) Adv. Nonlinear Stud., 14, pp. 619-629
  • Rossi, J.D., Saintier, N., On the first nontrivial eigenvalue of theoo-Laplacian with Neumann boundary conditions Houston J. Math, , to appear
  • Villani, C., Optimal transport (2009) Old and New Grundlehren Math. Wiss., 338. , Springer, Berlin

Citas:

---------- APA ----------
Del Pezzo, L., Rossi, J., Saintier, N. & Salort, A. (2015) . An optimal mass transport approach for limits of eigenvalue problems for the fractional p-Laplacian. Advances in Nonlinear Analysis, 4(3), 235-249.
http://dx.doi.org/10.1515/anona-2015-0013
---------- CHICAGO ----------
Del Pezzo, L., Rossi, J., Saintier, N., Salort, A. "An optimal mass transport approach for limits of eigenvalue problems for the fractional p-Laplacian" . Advances in Nonlinear Analysis 4, no. 3 (2015) : 235-249.
http://dx.doi.org/10.1515/anona-2015-0013
---------- MLA ----------
Del Pezzo, L., Rossi, J., Saintier, N., Salort, A. "An optimal mass transport approach for limits of eigenvalue problems for the fractional p-Laplacian" . Advances in Nonlinear Analysis, vol. 4, no. 3, 2015, pp. 235-249.
http://dx.doi.org/10.1515/anona-2015-0013
---------- VANCOUVER ----------
Del Pezzo, L., Rossi, J., Saintier, N., Salort, A. An optimal mass transport approach for limits of eigenvalue problems for the fractional p-Laplacian. Adv. Nonlinear Anal. 2015;4(3):235-249.
http://dx.doi.org/10.1515/anona-2015-0013