Remarks on an overdetermined boundary value problem |
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Authors: | A Farina B Kawohl |
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Institution: | 1.LAMFA, CNRS UMR 6140,Université de Picardie Jules Verne, Faculté de Mathématiques et d’Informatique,Amiens,France;2.Mathematisches Institut,Universit?t zu K?ln,K?ln,Germany |
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Abstract: | We modify and extend proofs of Serrin’s symmetry result for overdetermined boundary value problems from the Laplace-operator
to a general quasilinear operator and remove a strong ellipticity assumption in Philippin (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) and a growth assumption in Garofalo and Lewis (A symmetry result related to some overdetermined boundary
value problems, Am. J. Math. 111, 9–33, 1989) on the diffusion coefficient A, as well as a starshapedness assumption on Ω in Fragalà et al. (Overdetermined boundary value problems with possibly degenerate
ellipticity: a geometric approach. Math. Zeitschr. 254, 117–132, 2006). |
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Keywords: | 35J65 35B35 |
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