Open AccessAn Overdetermined Problem for an Elliptic Equation
Author(s) -
Robert Dalmasso
Publication year - 2010
Publication title -
publications of the research institute for mathematical sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.786
H-Index - 39
eISSN - 1663-4926
pISSN - 0034-5318
DOI - 10.2977/prims/19
Subject(s) - overdetermined system , mathematics , elliptic curve , mathematical analysis , calculus (dental) , algebra over a field , pure mathematics , medicine , dentistry
International audienceWe consider the following overdetermined boundary value problem: Δ u + λ u + μ = 0 in Ω, u = 0 on ∂Ω and ∂u/∂n = c on ∂Ω, where c ≠ 0, λ and μ are real constants and Ω ⊂ ℝ2 is a smooth bounded convex open set. We fi rst show that it may happen that the problem has no solution. Then we study the existence of solutions for a wide class of domains
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