Maximum principles and symmetry results for a class of fully nonlinear elliptic PDEs

Nonlinear Differential Equations and Applications

Volumn 17, Issue 5, 2010, Pages 591-600

  Enache, Cristian ^a  

^a OVIDIUS UNIVERSITY   (Romania)

Author keywords

A priori bounds; Fully nonlinear elliptic equations; Maximum principles; Overdetermined problems; Radial solutions

Indexed keywords

EID: 77957236644     PISSN: 10219722     EISSN: 14209004     Source Type: Journal    
DOI: 10.1007/s00030-010-0070-5     Document Type: Article

References (14)

1. Aviles P.: Symmetry theorems related to Pompeiu's problem. Amer. J. Math. 108, 1023-1036 (1986).
2. Brandolini B., Nitsch C., Salani P., Trombetti C.: Serrin type overdetermined problems: an alternative proof. Arch. Ration. Mech. Anal. 190, 267-280 (2008).
3. Hardy, G. H., Littlewood, J. E., Pólya, G.: Inequalities. Cambridge Mathematical Library. Cambridge University Press, Cambridge (1998).
4. Ma X.-N.: A necessary condition of solvability for the capillarity boundary of Monge-Ampère equations in two dimensions. Proc. Am. Math. Soc. 127, 763-769 (1999).
5. 3. J. Funct. Anal. 255, 1713-1723 (2008).
6. Payne L. E., Philippin G. A.: Some maximum principles for nonlinear elliptic equations in divergence form with applications to capillary surfaces and to surfaces of constant mean curvature. Nonlinear Anal. 3, 193-211 (1979).
7. Payne L. E., Schaefer P. W.: On overdetermined boundary value problems for the Biharmonic Operator. J. Math. Anal. Appl. 187, 598-616 (1994).
8. Philippin G. A., Safoui A.: Some maximum principle and symmetry results for a class of boundary value problems involving Monge-Ampère equation. Math. Models Methods Appl. Sci. 11, 1073-1080 (2001).
9. Philippin G. A., Safoui A.: Some applications of the maximum principle to a variety of fully nonlinear elliptic PDE's. Z. Angew. Math. Phys. 54, 739-755 (2003).
10. Protter M. H., Weinberger H. F.: Maximum principles in differential equations. Springer, Berlin (1975).
11. Reilly R. C.: On the Hessian of a function and the curvatures of its graph. Michigan Math. J. 20, 373-383 (1973).
12. Serrin J.: A symmetry problem in potential theory. Arch. Rational Mech. Anal. 43, 304-318 (1971).
13. Trudinger N. S.: On the Dirichlet problem for Hessian equations. Acta Math. 175, 151-164 (1995).
14. Trudinger N. S.: On new isoperimetric inequalities and symmetrization. J. Reine Angew. Math. 488, 203-220 (1997).