Artículo

Estamos trabajando para conseguir la versión final de este artículo
Consulte el artículo en la página del editor
Consulte la política de Acceso Abierto del editor

Abstract:

In this paper, we study the asymptotic behavior of the sequence of solutions for a family of torsional creep-type problems, involving inhomogeneous and anisotropic differential operators, on a bounded domain, subject to the homogenous Dirichlet boundary condition. We find out that the sequence of solutions converges uniformly on the domain to a certain distance function defined in accordance with the anisotropy of the problem. In addition, we identify the limit problem via viscosity solution theory. © 2018 Author(s).

Registro:

Documento: Artículo
Título:Inhomogeneous torsional creep problems in anisotropic Orlicz Sobolev spaces
Autor:Mihailescu, M.; Pérez-Llanos, M.
Filiación:Department of Mathematics, University of Craiova 200585 Craiova, Simion Stoilow Institute of Mathematics of the Romanian Academy, Bucharest, Romania, 010702, Romania
IMAS-CONICET and Departamento e Matemática, FCEyN UBA, Ciudad Universitaria, Pab 1, Buenos Aires, 1428, Argentina
Año:2018
Volumen:59
Número:7
DOI: http://dx.doi.org/10.1063/1.5047918
Título revista:Journal of Mathematical Physics
Título revista abreviado:J. Math. Phys.
ISSN:00222488
Registro:https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_00222488_v59_n7_p_Mihailescu

Referencias:

  • Adams, R.A., Sobolev Spaces (1975) Pure and Applied Mathematics, 65. , (Academic Press (A subsidiary of Harcourt Brace Jovanovich, Publishers), New York-London), MR 0450957
  • Aronsson, G., Extension of functions satisfying Lipschitz conditions (1967) Ark. Mat., 6, pp. 551-561. , MR 0217665
  • Belloni, M., Kawohl, B., The pseudo-p-Laplace eigenvalue problem and viscosity solutions as p → â (2004) ESAIM Control Optim. Calculus Var., 10 (1), pp. 28-52. , MR 2084254
  • Bhattacharya, T., Dibenedetto, E., Manfredi, J., Limits as p → â of Δpup = f and related extremal problems (1991) Rend. Semin. Mat. Univ. Politec. Torino, (SPECIAL ISSUE), pp. 15-68. , some topics in nonlinear PDEs (Turin, 1989). MR 1155453
  • Bocea, M., MihÄilescu, M., Γ-convergence of inhomogeneous functionals in Orlicz-Sobolev spaces (2015) Proc. Edinburgh Math. Soc. (2), 58 (2), pp. 287-303. , MR 3341440
  • Bocea, M., MihÄilescu, M., On a family of inhomogeneous torsional creep problems (2017) Proc. Am. Math. Soc., 145 (10), pp. 4397-4409. , MR 3690623
  • Braides, A., Γ-convergence for beginners (2002) Oxford Lecture Series in Mathematics and Its Applications, 22. , (Oxford University Press, Oxford), MR 1968440
  • Brezis, H., (2011) Functional Analysis, Sobolev Spaces and Partial Differential Equations, , (Universitext, Springer, New York), MR 2759829
  • Clément, P., De Pagter, B., Sweers, G., De Thélin, F., Existence of solutions to a semilinear elliptic system through Orlicz-Sobolev spaces (2004) Mediterr. J. Math., 1 (3), pp. 241-267. , MR 2094464
  • Crandall, M.G., Ishii, H., Lions, P.-L., User's guide to viscosity solutions of second order partial differential equations (1992) Bull. Am. Math. Soc., 27 (1), pp. 1-67. , MR 1118699
  • Dal Maso, G., An introduction to Γ-convergence (1993) Progress in Nonlinear Differential Equations and Their Applications, 8. , (Birkhäuser Boston, Inc., Boston, MA), MR 1201152
  • De Giorgi, E., Sulla convergenza di alcune successioni d'integrali del tipo dell'area (1975) Rend. Mat., 8 (6), pp. 277-294. , Collection of articles dedicated to Mauro Picone on the occasion of his ninetieth birthday, MR 0375037
  • De Giorgi, E., Franzoni, T., Su un tipo di convergenza variazionale (1975) Atti Accad. Naz. Lincei Rend. Cl. Sci. Fis. Mat. Natur. (8), 58 (6), pp. 842-850. , MR 0448194
  • Di Castro, A., Pérez-Llanos, M., Urbano, J.M., Limits of anisotropic and degenerate elliptic problems (2012) Commun. Pure Appl. Anal., 11 (3), pp. 1217-1229. , MR 2968618
  • Fukagai, N., Ito, M., Narukawa, K., Positive solutions of quasilinear elliptic equations with critical Orlicz-Sobolev nonlinearity on R N (2006) Funkcialaj Ekvacioj, 49 (2), pp. 235-267. , MR 2271234
  • Ishibashi, T., Koike, S., On fully nonlinear PDEs derived from variational problems of Lp norms (2001) SIAM J. Math. Anal., 33 (3), pp. 545-569. , MR 1871409
  • Ishii, H., A simple, direct proof of uniqueness for solutions of the Hamilton-Jacobi equations of eikonal type (1987) Proc. Am. Math. Soc., 100 (2), pp. 247-251. , MR 884461
  • Jensen, R., Uniqueness of Lipschitz extensions: Minimizing the sup norm of the gradient (1993) Arch. Ration. Mech. Anal., 123 (1), pp. 51-74. , MR 1218686
  • Jost, J., Li-Jost, X., Calculus of variations (1998) Cambridge Studies in Advanced Mathematics, 64. , (Cambridge University Press, Cambridge), MR 1674720
  • Juutinen, P., Minimization problems for Lipschitz functions via viscosity solutions (1998) Ann. Acad. Sci. Fenn. Math. Diss., 115, p. 53. , MR 1632063
  • Juutinen, P., (1998), Ph.D. dissertation (University of Jyväskulä, Jyväskulä); Juutinen, P., Lindqvist, P., Manfredi, J.J., The â-eigenvalue problem (1999) Arch. Ration. Mech. Anal., 148 (2), pp. 89-105. , MR 1716563
  • Juutinen, P., Lindqvist, P., Manfredi, J.J., On the equivalence of viscosity solutions and weak solutions for a quasi-linear equation (2001) SIAM J. Math. Anal., 33 (3), pp. 699-717. , MR 1871417
  • Kawohl, B., On a family of torsional creep problems (1990) J. Reine Angew. Math., 410, pp. 1-22. , MR 1068797
  • Lieberman, G.M., The natural generalization of the natural conditions of Ladyzhenskaya and Ural'tseva for elliptic equations (1991) Commun. Partial Differ. Equations, 16 (2-3), pp. 311-361. , MR 1104103
  • Martí Nez, S., Wolanski, N., A minimum problem with free boundary in Orlicz spaces (2008) Adv. Math., 218 (6), pp. 1914-1971. , MR 2431665
  • Payne, L.E., Philippin, G.A., Some applications of the maximum principle in the problem of torsional creep (1977) SIAM J. Appl. Math., 33 (3), pp. 446-455. , MR 0455738
  • Pérez-Llanos, M., Anisotropic variable exponent (p(·), q(·))-Laplacian with large exponents (2013) Adv. Nonlinear Stud., 13 (4), pp. 1003-1034. , MR 3115150
  • Pérez-Llanos, M., Rossi, J.D., The behaviour of the p(x)-Laplacian eigenvalue problem as p(x) → â (2010) J. Math. Anal. Appl., 363 (2), pp. 502-511. , MR 2564871
  • Perez-Llanos, M., Rossi, J.D., The limit as p(x) → â of solutions to the inhomogeneous Dirichlet problem of the p(x)-Laplacian (2010) Nonlinear Anal., 73 (7), pp. 2027-2035. , MR 2674182

Citas:

---------- APA ----------
Mihailescu, M. & Pérez-Llanos, M. (2018) . Inhomogeneous torsional creep problems in anisotropic Orlicz Sobolev spaces. Journal of Mathematical Physics, 59(7).
http://dx.doi.org/10.1063/1.5047918
---------- CHICAGO ----------
Mihailescu, M., Pérez-Llanos, M. "Inhomogeneous torsional creep problems in anisotropic Orlicz Sobolev spaces" . Journal of Mathematical Physics 59, no. 7 (2018).
http://dx.doi.org/10.1063/1.5047918
---------- MLA ----------
Mihailescu, M., Pérez-Llanos, M. "Inhomogeneous torsional creep problems in anisotropic Orlicz Sobolev spaces" . Journal of Mathematical Physics, vol. 59, no. 7, 2018.
http://dx.doi.org/10.1063/1.5047918
---------- VANCOUVER ----------
Mihailescu, M., Pérez-Llanos, M. Inhomogeneous torsional creep problems in anisotropic Orlicz Sobolev spaces. J. Math. Phys. 2018;59(7).
http://dx.doi.org/10.1063/1.5047918