A Symmetry Result Related to Some Overdetermined Boundary Value Problems

1989/02/01 by Nicola Garofalo, John L. Lewis · 131 citations
Computer Science · Engineering · Mathematics · #Advanced Mathematical Modeling in Engineering #Boundary value problem #Geometry #Mathematical analysis #Mathematics #Nonlinear Partial Differential Equations #Overdetermined system #Pure mathematics #Stability and Controllability of Differential Equations #Statistics #Symmetry (geometry) #Value (mathematics)

paper · doi:10.2307/2374477

published in American Journal of Mathematics 111(1), 9 (Johns Hopkins University Press)

openalex publication_date 1989/02/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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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Related

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