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Soluciones simétricas de algunos problemas elípticos

Quintero H., José Raúl (2012) Soluciones simétricas de algunos problemas elípticos. Revista Colombiana de Matemáticas; Vol. 27, núm. 1-2 (1993); 95-109 0034-7426 .

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In this paper we study solutions to the Neumann problem (I)         ∆u=  F(u)   in Ω,    ∂u/∂n =  G(u)  on Ω,                                                and the Dirichlet problema      (II)    ∆u=F(u)   in  Ω,               u=c        n  ∂Ω      where Ω is a bounded domain in Rn with a smooth boundary ∂ Ω  ∂/ ∂n is the derivative with respect to the outward normal n and c ϵ R. If  Ω is the unit ball and if either F(t) = f(t) and G(t) = g(t) or F(t) = /(t) . t and G(t) = 9(t) . t where f is a strictly increasing continuous function and  g is a strictly decreasing continuous function, we prove that solutions to problems (I) and (II) are radially symmetric about the origen. If Ω  is the unit ball and F is a continuous function that does not change sign, we prove that solutions of (II) are radially symmetric about the origen. If Ω ⊂ Rn  is a symmetric bounded domain with respect to a hyperplane T and f ϵ C(Ω x R,R), g ϵC (∂Ω x R, R) are functions that satisfy the same monoton..icity properties in the second variable as before, then we prove that solutions are symmetric with respect to the hyperplane T. If F satisfies the same condition as in the first case and G ≡ 0, we prove that the only solutions of (I) are constant functions. Furthermore, we find a formula for solutions of (I) in the unitary ball that allow us to deduce some non-existence results. We find conditions on F and G in order for (I) to have no solutions in any bounded domain.

Tipo de documento:Artículo - Article
Palabras clave:Bounded domain; soft limit, derivative; continuous function; hyperplane
Unidad administrativa:Revistas electrónicas UN > Revista Colombiana de Matemáticas
Código ID:33689
Enviado por : Dirección Nacional de Bibliotecas STECNICO
Enviado el día :01 Julio 2014 10:16
Ultima modificación:18 Agosto 2014 20:24
Ultima modificación:18 Agosto 2014 20:24
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