A Symmetry Result Related to Some Overdetermined Boundary Value Problems

1989/02/01 by Nicola Garofalo, John L. Lewis · 10 citations
Computer Science · Mathematics · Engineering · #Advanced Mathematical Modeling in Engineering #Nonlinear Partial Differential Equations #Stability and Controllability of Differential Equations

paper · doi:10.2307/2374477

Abstract

Soit ΩCR n un ensemble ouvert connexe borne et on suppose pour p fixe, 1 0, on suppose que |⊇u(x)|→a, u(x)→0 quand x→∂Ω au sens suivant: etant donne e>0, il existe un ensemble ouvert 0=O(e)⊃∂Ω tel que ∥⊇u(x)|−a|<e, u(x)<e, pour presque tout x∈0∩Ω par rapport a la mesure de Lebesgue n. Alors Ω est une boule et u est radialement symetrique autour du centre de la boule

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• Symmetry for a general class of overdetermined elliptic problems
• Radial symmetry and partially overdetermined problems in a convex cone
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