The Neumann problem for singular fully nonlinear operators

Journal des Mathematiques Pures et Appliquees

Volumn 90, Issue 3, 2008, Pages 286-311

  Patrizi, Stefania ^a  

^a SAPIENZA UNIVERSITY OF ROME   (Italy)

Author keywords

Fully nonlinear operators; Maximum principle; Neumann problem; Principal eigenvalue; Viscosity solutions

Indexed keywords

EID: 49549124026     PISSN: 00217824     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.matpur.2008.04.007     Document Type: Article

References (19)

1. Anane A. Simplicite et isolation de la premiere valeur propre du p-laplacien avec poids (Simplicity and isolation of the first eigenvalue of the p-Laplacian with weight). C. R. Acad. Sci. Paris Ser. I Math. 305 16 (1987) 725-728 (in French)
2. Barles G. Fully nonlinear Neumann type boundary conditions for second-order elliptic and parabolic equations. J. Differential Equations 106 1 (1993) 90-106
3. Barles G. Nonlinear Neumann boundary conditions for quasilinear degenerate elliptic equations and applications. J. Differential Equations 154 (1999) 191-224
4. Barles G., and Da Lio F. On the boundary ergodic problem for fully nonlinear equations in bounded domains with general nonlinear Neumann boundary conditions. Ann. I. H. Poincaré 22 (2005) 501-541
5. Barles G., and Ramaswamy M. Sufficient structure conditions for uniqueness of viscosity solutions of semilinear and quasilinear equations. NoDEA 12 4 (2006) 503-523
6. Berestycki H., Nirenberg L., and Varadhan S.R.S. The principal eigenvalue and maximum principle for second order elliptic operators in general domain. Comm. Pure Appl. Math. 47 1 (1994) 47-92
7. Birindelli I., and Demengel F. Eigenvalue, maximum principle and regularity for fully nonlinear homogeneous operators. Comm. Pure Appl. Anal. 6 2 (2007) 335-366
8. Busca J., Esteban M.J., and Quaas A. Nonlinear eigenvalues and bifurcation problems for Pucci's operators. Ann. Inst. H. Poincaré Anal. Non Lineaire 22 2 (2005) 187-206
9. Caffarelli L., and Cabr X. Fully Nonlinear Equations. Colloquium Publications vol. 43 (1995), American Mathematical Society, Providence, RI
10. Crandall M.C., Ishii H., and Lions P.L. User's guide to viscosity solutions of second order partial differential equations. Bull. Amer. Math. Soc. (N.S.) 27 1 (1992) 1-67
11. Ishii H. Fully nonlinear oblique derivative problems for nonlinear second-order elliptic PDE's. Duke Math. J. 62 3 (1991) 633-661
12. Ishii H. Perron's method for Hamilton-Jacobi equations. Duke Math. J. 55 (1987) 369-384
13. Ishii H., and Lions P.L. Viscosity solutions of fully nonlinear second-order elliptic partial differential equations. J. Differential Equations 83 1 (1990) 26-78
14. H. Ishii, Y. Yoshimura, Demi-eigenvalues for uniformly elliptic Isaacs operators, preprint
15. Lions P.L. Bifurcation and optimal stochastic control. Nonlinear Anal. 7 2 (1983) 177-207
16. P. Lindqvist, Notes on the p-Laplace equation, Report, University of Jyvskyl Department of Mathematics and Statistics, vol. 102 University of Jyvskyl, Jyvskyl, 2006, ii+80 pp
17. P. Lindqvist, On a nonlinear eigenvalue problem, in: Fall. School in Analysis (Jyväskylä, 1994), Report, 68, Univ. Jyväskylä, Jyväskylä, 1995, pp. 33-54
18. Quaas A. Existence of positive solutions to a "semilinear" equation involving the Pucci's operators in a convex domain. Differential Integral Equations 17 5-6 (2004) 481-494
19. Quaas A., and Sirakov B. On the principal eigenvalues and the Dirichlet problem for fully nonlinear operators. C. R. Math. Acad. Sci. Paris 342 2 (2006) 115-118