Large solutions to elliptic equations involving fractional Laplacian

Annales de l'Institut Henri Poincare (C) Analyse Non Lineaire

Volumn 32, Issue 6, 2015, Pages 1199-1228

  Chen, Huyuan ^a,b   Felmer, Patricio ^b   Quaas, Alexander ^c  

^a JIANGXI NORMAL UNIVERSITY   (China)

^b UNIVERSITY OF CHILE   (Chile)

^c DEPARTAMENTO DE FÍSICA   (Chile)

Author keywords

Existence; Fractional Laplacian; Large solutions; Non existence infinite existence; Uniqueness

Indexed keywords

NONLINEAR ANALYSIS;

EXISTENCE; FRACTIONAL LAPLACIAN; LARGE SOLUTIONS; NON-EXISTENCE; UNIQUENESS;

LAPLACE TRANSFORMS;

EID: 84948065191     PISSN: 02941449     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.anihpc.2014.08.001     Document Type: Article

References (33)

1. N. Abatangelo Large s-harmonic functions and boundary Blow-up solutions for the fractional Laplacian arXiv:1310.3193 [math.AP]
2. J.M. Arrieta A. Rodríguez-Bernal Localization on the boundary of blow-up for reaction-diffusion equations with nonlinear boundary conditions Commun. Partial Differ. Equ. 29 2004 1127 1148
3. C. Bandle M. Marcus Large solutions of semilinear elliptic equations: Existence, uniqueness and asymptotic behaviour J. Anal. Math. 58 1992 9 24
4. C. Bandle M. Marcus Dependence of blowup rate of large solutions of semilinear elliptic equations on the curvature of the boundary Complex Var. Theory Appl. 49 2004 555 570
5. X. Cabré L. Caffarelli Fully Nonlinear Elliptic Equation Colloq. Publ.-Am. Math. Soc. vol. 43 1995
6. L. Caffarelli L. Silvestre Regularity theory for fully nonlinear integro-differential equations Commun. Pure Appl. Math. 62 5 2009 597 638
7. L. Caffarelli L. Silvestre Regularity results for nonlocal equations by approximation Arch. Ration. Mech. Anal. 200 1 2011 59 88
8. L. Caffarelli L. Silvestre The Evans-Krylov theorem for nonlocal fully non linear equations Ann. Math. 174 2 2011 1163 1187
9. G. Barles C. Imbert Second-order elliptic integro-differential equations: viscosity solutions theory revisited Ann. Henri Poincaré 25 2008 567 585
10. H. Chen, P. Felmer, Liouville Property for fully nonlinear integral equation in exterior domain, preprint.
11. M. Chuaqui C. Cortázar M. Elgueta J. García-Melián Uniqueness and boundary behaviour of large solutions to elliptic problems with singular weights Commun. Pure Appl. Anal. 3 2004 653 662
12. M. del Pino R. Letelier The influence of domain geometry in boundary blow-up elliptic problems Nonlinear Anal. 48 6 2002 897 904
13. G. Díaz R. Letelier Explosive solutions of quasilinear elliptic equations: existence and uniqueness Nonlinear Anal. 20 2 1993 97 125
14. Y. Du Q. Huang Blow-up solutions for a class of semilinear elliptic and parabolic equations SIAM J. Math. Anal. 31 1999 1 18
15. P. Felmer A. Quaas Boundary blow up solutions for fractional elliptic equations Asymptot. Anal. 78 3 2012 123 144
16. P. Felmer A. Quaas J. Tan Positive solutions of nonlinear Schrodinger equation with the fractional Laplacian Proc. R. Soc. Edinb., Sect. A, Math. 142 2012 1 26
17. P. Felmer A. Quaas Fundamental solutions and two properties of elliptic maximal and minimal operators Trans. Am. Math. Soc. 361 11 2009 5721 5736
18. P. Felmer A. Quaas Fundamental solutions and Liouville type theorems for nonlinear integral operators Adv. Math. 226 2011 2712 2738
19. P. Felmer A. Quaas Fundamental solutions for a class of Isaacs integral operators Discrete Contin. Dyn. Syst. 30 2 2011 493 508
20. J. García-Melián Nondegeneracy and uniqueness for boundary blow-up elliptic problems J. Differ. Equ. 223 1 2006 208 227
21. J. García-Meliían R. Gómez-Reñasco J. López-Gómez J. Sabina de Lis Pointwise growth and uniqueness of positive solutions for a class of sublinear elliptic problems where bifurcation from infinity occurs Arch. Ration. Mech. Anal. 145 3 1998 261 289
22. J.B. Keller On solutions of δu = f(u), Commun. Pure Appl. Math. 10 1957 503 510
23. S. Kim, A note on boundary blow-up problem of δu =up, IMA preprint, No. 1872, 2002.
24. C. Loewner L. Nirenberg Partial differential equations invariant under conformal projective transformations Contributions to Analysis 1974 Academic Press New York 245 272 a collection of papers dedicated to Lipman Bers
25. M. Marcus L. Véron Existence and uniqueness results for large solutions of general nonlinear elliptic equation J. Evol. Equ. 3 2003 637 652
26. M. Marcus L. Véron Uniqueness and asymptotic behavior of solutions with boundary blow-up for a class of nonlinear elliptic equations Ann. Inst. Henri Poincaré 14 2 1997 237 274
27. R. Osserman On the inequality δu =f(u) Pac. J. Math. 7 1957 1641 1647
28. G. Palatucci O. Savin E. Valdinoci Local and global minimizers for a variational energy involving a fractional norm Ann. Mat. Pura Appl. (4) 192 2013 673 718
29. V. Râdulescu Singular phenomena in nonlinear elliptic problems: from blow-up boundary solutions to equations with singular nonlinearities Handbook of Differential Equations: Stationary Partial Differential Equations, vol. 4 2007 485 593
30. X. Ros-Oton J. Serra The Dirichlet problem for the fractional Laplacian, regularity up to the boundary J. Math. Pures Appl. 101 3 2014 275 302
31. R. Servadei E. Valdinoci Weak and viscosity solutions of the fractional Laplace equation Publ. Mat. 58 1 2014 133 154
32. L. Silvestre Hölder estimates for solutions of integro differential equations like the fractional Laplace Indiana Univ. Math. J. 55 2006 1155 1174
33. E.M. Stein Singular Integrals and Differentiability Properties of Functions 1970 Princeton University Press