Boundary blow up solutions for fractional elliptic equations

Asymptotic Analysis

Volumn 78, Issue 3, 2012, Pages 123-144

  Felmer, Patricio ^a   Quaas, Alexander ^b  

^a UNIVERSITY OF CHILE   (Chile)

^b DEPARTAMENTO DE FÍSICA   (Chile)

Author keywords

boundary blow up; fractional Laplacian; Isaacs operators; subsolution; supersolution

Indexed keywords

BLOW-UP; BLOWUP SOLUTIONS; BOUNDARY VALUES; BOUNDED DOMAIN; ELLIPTIC EQUATIONS; EXISTENCE OF A SOLUTIONS; LAPLACIANS; NONLINEAR OPERATOR; SUBSOLUTION; SUPERSOLUTION;

ASYMPTOTIC ANALYSIS;

MATHEMATICAL TECHNIQUES;

EID: 84863430024     PISSN: 09217134     EISSN: None     Source Type: Journal    
DOI: 10.3233/ASY-2011-1081     Document Type: Article

References (22)

1. C. Bandle and M. Marcus, 'Large' solutions of semilinear elliptic equations: Existence, uniqueness and asymptotic behaviour, J. Anal. Math. 58 (1992), 9-24.
2. C. Bandle and M. Marcus, Dependence of blowup rate of large solutions of semilinear elliptic equations on the curvature of the boundary, Complex Variables Theory Appl. 49 (2004), 555-570. (Pubitemid 39250322)
3. G. Barles, E. Chasseigne and C. Imbert, On the Dirichlet problem for second-order elliptic integro-differential equations, Indiana Univ. Math. J. 57 (2008), 213-246.
4. H. Brezis, Semilinear equations in RN without condition at infinity, Appl. Math. Optim. 12 (1984), 271-282.
5. X. Cabré and L. Caffarelli, Fully Nonlinear Elliptic Equation, Vol. 43, American Mathematical Society, Colloquium Publication, 1995.
6. L. Caffarelli and L. Silvestre, Regularity theory for fully nonlinear integro-differential equations, Communications on Pure and Applied Mathematics 62(5) (2009), 597-638.
7. L.A. Caffarelli and L. Silvestre, Regularity results for nonlocal equations by approximation, Arch. Ration. Mech. Anal. 200(1) (2011), 59-88.
8. L.A. Caffarelli and L. Silvestre, The Evans-Krylov theorem for non local fully non linear equations, Annals of Mathematics 174(2) (2011), 1163-1187.
9. M.G. Crandall, M. Kocan, P.L. Lions and A. Swiech, Existence results for boundary problems for uniformly elliptic and parabolic fully nonlinear equations, Electron. J. Differential Equations 24 (1999), 1-20. (Pubitemid 38994915)
10. M. Del Pino and R. Letelier, The influence of domain geometry in boundary blow-up elliptic problems, Nonlinear Analysis: Theory, Methods and Applications 48(6) (2002), 897-904. (Pubitemid 33112514)
11. G. Diaz and J.I. Diaz, Uniqueness of the boundary behavior for large solutions to a degenerate elliptic equation involving the8-Laplacian, Rev. R. Acad. Cien. Serrie A Mat. 97(3) (2003), 455-460.
12. G. Díaz and R. Letelier, Explosive solutions of quasilinear elliptic equations: Existence and uniqueness, Nonlinear Analysis: Theory, Methods and Applications 20(2) (1993), 97-125.
13. M. Esteban, P. Felmer and A. Quaas, Super-linear elliptic equation for fully nonlinear operators without growth restrictions for the data, Proc. Roy. Soc. Edinburgh 53 (2010), 125-141.
14. P. Felmer and A. Quaas, Fundamental solutions and Liouville type theorems for nonlinear integral operators, Advances in Mathematics 226(3) (2011), 2712-2738.
15. H. Ishii, On uniqueness and existence of viscosity solutions of fully nonlinear second-order elliptic PDEs, Comm. Pure Appl. Math. 42(1) (1989), 15-45.
16. J.B. Keller, On solutions of Äu = f(u), Comm. Pure Appl. Math. 10 (1957), 503-510.
17. V. Kondrat'ev and V. Nikishkin, Asymptotics, near the boundary of a solution of a singular boundary value problems for semilinear elliptic equations, Differential Equations 26 (1990), 345-348.
18. C. Loewner and L. Nirenberg, Partial differential equations invariant under conformal projective transformations, in: Contributions to Analysis (a Collection of Papers Dedicated to Lipman Bers), Academic Press, New York, 1974, pp. 245- 272.
19. M. Marcus and L. Veron, Uniqueness and asymptotic behavior of solutions with boundary blow-up for a class of nonlinear elliptic equations, Ann. Inst. H. Poincaré 14 (1997), 237-274. (Pubitemid 127382465)
20. R. Osserman, On the inequality Äu -f(u), Pacific J. Math. 7 (1957), 1641-1647.
21. V. Řadulescu, Singular phenomena in nonlinear elliptic problems: from boundary blow-up solutions to equations with singular nonlinearities, in: Handbook of Differential Equations: Stationary Partial Differential Equations, M. Chipot, ed., Vol. 4, 2007, pp. 483-591.
22. L. Silvestre, Hölder estimates for solutions of integro differential equations like the fractional laplace, Indiana Univ. Math. J. 55 (2006), 1155-1174. (Pubitemid 44214081)