Convexity estimates for nonlinear elliptic equations and application to free boundary problems;Estimations de convexité pour des équations elliptiques non linéaires et application à des problèmes de frontière libre

Comptes Rendus de l'Academie des Sciences - Series I: Mathematics

Volumn 331, Issue 10, 2000, Pages 771-776

  Dolbeault, Jean ^a   Monneau, Régis ^b  

^a UNIVERSITÉ PARIS DAUPHINE   (France)

^b UNIVERSITÉ PARIS EST   (France)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0034668480     PISSN: 07644442     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0764-4442(00)01732-8     Document Type: Article

References (9)

1. [1] Caffarelli L.A., Compactness method in free boundary problems, Commun. Partial Differ. Eq. 5 (4) (1980) 427-448.
2. [2] Caffarelli L.A., Spruck J., Convexity properties of solutions to some classical variational problems, Commun. Partial Differ. Eq. 7 (11) (1982) 1337-1379.
3. [3] Dolbeault J., Monneau R., Convexity properties of the free boundary and gradient estimates for quasi-linear elliptic equations, Preprint.
4. [4] Friedman A., Variational Principles and Free Boundary Problems, Pure and Applied Mathematics, ISSN 0079-8185, Wiley-Interscience, 1982.
5. [5] Friedman A., Phillips D., The free boundary of a semilinear elliptic equation, Trans. Amer. Math. Soc. 282 (1984) 153-182.
6. [6] Kawohl B., When are solutions to nonlinear elliptic boundary value problems convex, Commun. Partial Differ. Eq. 10 (1985) 1213-1225.
7. [7] Kinderlehrer D., Nirenberg L., Regularity in free boundary problems, Bull. Amer. Math. Soc. 7 (1982) 65-222.
8. [8] Rodrigues J.F., Obstacle Problems in Mathematical Physics, North-Holland, 1987.
9. [9] Talenti G., Some estimates of solutions to Monge-Ampère type equations in dimension two, Ann. Scuola Norm. Sup. Pisa Cl. Sci, IV. Ser. 8 (1981) 183-230.