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Abstract:

We study existence of large solutions, that is, solutions that verify u(x)→+ ∞ as x→ ∂. Ω, for equations like. -I(u,x)+u(x)p= 0,x∈Ω, where Ω is a bounded smooth domain in RN, p> 1 and I is a nonlocal operator of the form, where α. ∈ (0, 2) and ρ:Ω-→R is a function whose main particularity is that 0 < ρ(x) ≤ dist(x, ∂ Ω). We also obtain uniqueness of the solution in a class of large solutions whose blow-up rate depends on p, α and the rate at which ρ shrinks near the boundary. © 2016 Elsevier Inc.

Registro:

Documento: Artículo
Título:Large solutions for a class of semilinear integro-differential equations with censored jumps
Autor:Rossi, J.D.; Topp, E.
Filiación:Departamento de Matemática, FCEyN Universidad de Buenos Aires, Ciudad Universitaria, Pab 1 (1428), Buenos Aires, Argentina
Departamento de Matemática y C.C., Universidad de Santiago de Chile, Casilla: 307, Santiago, Chile
Palabras clave:Large solutions; Nonlocal diffusion
Año:2016
Volumen:260
Número:9
Página de inicio:6872
Página de fin:6899
DOI: http://dx.doi.org/10.1016/j.jde.2016.01.016
Título revista:Journal of Differential Equations
Título revista abreviado:J. Differ. Equ.
ISSN:00220396
CODEN:JDEQA
Registro:https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_00220396_v260_n9_p6872_Rossi

Referencias:

  • Bandle, C., Marcus, M., Dependence of blow-up rate of large solutions of semilinear elliptic equations on the curvature of the boundary (2004) Complex Var. Theory Appl., 49, pp. 555-570
  • Barles, G., Chasseigne, E., Imbert, C., Hölder continuity of solutions of second-order non-linear elliptic integro-differential equations (2011) J. Eur. Math. Soc. (JEMS), 13, pp. 1-26
  • Barles, G., Chasseigne, E., Imbert, C., On the Dirichlet problem for second order elliptic integro-differential equations (2008) Indiana Univ. Math. J., 57 (1), pp. 213-246
  • Barles, G., Imbert, C., Second-order elliptic integro-differential equations: viscosity solutions' theory revisited (2008) Ann. Inst. H. Poincaré, Anal. Non Linéaire, 25 (3), pp. 567-585
  • Barles, G., Perthame, B., Exit time problems in optimal control and vanishing viscosity method (1988) SIAM J. Control Optim., 26, pp. 1133-1148
  • Barles, G., Perthame, B., Comparison principle for Dirichlet type Hamilton-Jacobi Equations and singular perturbations of degenerated elliptic equations (1990) Appl. Math. Optim., 21, pp. 21-44
  • Caffarelli, L., Silvestre, L., Regularity theory for nonlocal integro-differential equations (2009) Comm. Pure Appl. Math., 62 (5), pp. 597-638
  • Caffarelli, L., Silvestre, L., Regularity results for nonlocal equation by approximation (2011) Arch. Ration. Mech. Anal., 200 (1), pp. 59-88
  • Chen, H., Felmer, P., Quaas, A., Large solutions to elliptic equations involving fractional Laplacian preprint; Chuaqui, M., Cortázar, C., Elgueta, M., García-Melián, J., Uniqueness and boundary behavior of large solutions to elliptic problems with singular weights (2004) Commun. Pure Appl. Anal., 3, pp. 653-662
  • 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
  • Del Pino, M., Letelier, R., The influence of domain geometry in boundary blow-up elliptic problems (2002) Nonlinear Anal., Theory Methods Appl., 48 (6), pp. 897-904
  • Dynkin, E.B., Superprocesses and partial differential equations (1993) Ann. Probab., 21, pp. 1185-1262
  • Di Neza, E., Palatucci, G., Valdinoci, E., Hitchhiker's guide to the fractional slobber spaces (2012) Bull. Sci. Math., 136 (5), pp. 521-573
  • Felmer, P., Quaas, A., Boundary blow-up solutions for fractional elliptic equations (2012) Asymptot. Anal., 78, pp. 123-144
  • Gilbarg, D., Trudinger, N.S., (2001) Elliptic Partial Differential Equations of Second Order, , Springer-Verlag, Berlin
  • Ishii, H., Perron's method for Hamilton-Jacobi equations (1987) Duke Math. J., 55, pp. 369-384
  • Ishii, H., Nakamura, G., A class of integral equations and approximation of p-Laplace equations (2010) Calc. Var. Partial Differ. Equ., 37 (3-4), pp. 485-522
  • Juutinen, P., Rossi, J.D., Large solutions for the infinity Laplacian (2008) Adv. Calc. Var., 1 (3), pp. 271-289
  • Keller, J.B., On solutions of δu=f(u) (1957) Comm. Pure Appl. Math., 10, pp. 503-510
  • Lasry, J.M., Lions, P.L., Nonlinear elliptic equations with singular boundary conditions and stochastic control with state constraints (1989) Math. Ann., 283, pp. 583-630
  • Le Gall, F., Probabilistic approach to a class of semilinear partial differential equations (2007) Contemp. Math., 446, pp. 255-272. , AMS, Providence, RI, Perspectives in Nonlinear Partial Differential Equations
  • Loewner, C., Nirenberg, L., Partial differential equations invariant under conformal projective transformations (1974) Contributions to Analysis (Collection of Papers Dedicated to Lipman Bers), pp. 245-272. , Academic Press, New York
  • Marcus, M., Véron, L., Existence and uniqueness results for large solutions of general nonlinear elliptic equation (2003) J. Evol. Equ., 3, pp. 637-652
  • Marcus, M., Véron, L., Uniqueness and asymptotic behavior of solutions with boundary blow-up for a class of nonlinear elliptic equations (1997) Ann. Inst. H. Poincaré, Anal. Non Linéaire, 14 (2), pp. 237-274
  • Osserman, R., On the inequality δu≥f(u) (1957) Pacific J. Math., 7, pp. 1641-1647
  • Radulescu, V., Singular phenomena in nonlinear elliptic problems: from blow-up boundary solutions to equations with singular nonlinearities (2007) Handbook of Differential Equations: Stationary Partial Differential Equations, 4, pp. 485-593
  • Andreu-Vaillo, F., Mazon, J.M., Rossi, J.D., Toledo-Melero, J.J., Nonlocal Diffusion Problems (2010) Math. Surveys Monogr., 165. , AMS, Providence, RI
  • Bandle, C., Marcus, M., "Large" solutions of semilinear elliptic equations: existence, uniqueness and symptotic behaviour (1992) J. D'Anal. Math., 58, pp. 9-24

Citas:

---------- APA ----------
Rossi, J.D. & Topp, E. (2016) . Large solutions for a class of semilinear integro-differential equations with censored jumps. Journal of Differential Equations, 260(9), 6872-6899.
http://dx.doi.org/10.1016/j.jde.2016.01.016
---------- CHICAGO ----------
Rossi, J.D., Topp, E. "Large solutions for a class of semilinear integro-differential equations with censored jumps" . Journal of Differential Equations 260, no. 9 (2016) : 6872-6899.
http://dx.doi.org/10.1016/j.jde.2016.01.016
---------- MLA ----------
Rossi, J.D., Topp, E. "Large solutions for a class of semilinear integro-differential equations with censored jumps" . Journal of Differential Equations, vol. 260, no. 9, 2016, pp. 6872-6899.
http://dx.doi.org/10.1016/j.jde.2016.01.016
---------- VANCOUVER ----------
Rossi, J.D., Topp, E. Large solutions for a class of semilinear integro-differential equations with censored jumps. J. Differ. Equ. 2016;260(9):6872-6899.
http://dx.doi.org/10.1016/j.jde.2016.01.016