Remarks on an overdetermined boundary value problem

Calculus of Variations and Partial Differential Equations

Volumn 31, Issue 3, 2008, Pages 351-357

  Farina, A ^a   Kawohl, B ^b  

^a Faculté de Mathématiques et d Informatique   (France)

^b UNIVERSITY OF COLOGNE   (Germany)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 37349011126     PISSN: 09442669     EISSN: None     Source Type: Journal    
DOI: 10.1007/s00526-007-0115-8     Document Type: Article

References (17)

1. Alexandrov A.D. (1962). A characteristic property of the spheres. Ann. Mat. Pura Appl. 58: 303-354
2. Brock F. and Henrot A. (2002). A symmetry result for an overdetermined elliptic problem using continuous rearrangement and domain derivative. Rend. Circ. Mat. Palermo 51: 375-390
3. Degiovanni M., Musesti A. and Squassina M. (2003). On the regularity of solutions in the Pucci-Serrin identity. Calculus Variations 18: 317-334
4. Fragalà I., Gazzola F. and Kawohl B. (2006). Overdetermined boundary value problems with possibly degenerate ellipticity: a geometric approach. Math. Zeitschr. 254: 117-132
5. Garofalo N. and Lewis J.L. (1989). A symmetry result related to some overdetermined boundary value problems. Am. J. Math. 111: 9-33
6. Kawohl, B.: Symmetrization - or how to prove symmetry of solutions to partial differential equations. In: Jäger, W., Nečas, J., John, O., Najzar, K., Stara, J. (eds.) Partial Differential Equations, Theory and Numerical Solution. Chapman & Hall CRC Research Notes in Math. 406 London, pp. 214-229 (1999)
7. Lieberman G. (1988). Boundary regularity for solutions of degenerate elliptic equations. Nonlin. Anal. 12: 1203-1219
8. Payne L.A. and Philippin G.A. (1979). Some maximum principles for nonlinear elliptic equations in divergence form with applications to capillary surfaces and to surfaces of constant mean curvature. Nonlin. Anal. 3: 193-211
9. Philippin, G.A.: Applications of the maximum principle to a variety of problems involving elliptic differential equations, In: Schaefer, P.W. Maximum principles and eigenvalue problems in partial differential equations (Knoxville, TN, 1987), Longman Sci. Tech., Pitman Res. Notes Math. Ser., Harlow, 175, pp. 34-48 (1988)
10. Pohožaev S.J. (1965). Eigenfunctions of the equation Δu + λ f(u) = 0. Sov. Math. Doklady 6: 1408-1411
11. Prajapat J. (1998). Serrin's result for domains with a corner or cusp. Duke Math. J. 91: 29-31
12. Pucci P. and Serrin J. (1986). A general variational identity. Indiana Univ. Math. J. 35: 681-703
13. Rellich F. (1940). Darstellung der Eigenwerte von Δu + λ u = 0 durch ein Randintegral. Math. Zeitschr. 46: 635-636
14. Serrin J. (1971). A symmetry problem in potential theory. Arch. Ration. Mech. Anal. 43: 304-318
15. Sperb R. (1981). Maximum Principles and Applications. Academic
16. Thorbergsson G. (2000). A survey on isoparametric hypersurfaces and their generalizations. In: Dillen, F.J.E. and Verstraelen, L.C.A. (eds) Handbook of differential geometry, vol I., pp 963-995. North-Holland, Amsterdam
17. Weinberger H. (1971). Remark on the preceding paper of Serrin. Arch. Ration. Mech. Anal. 43: 319-320