DOI: http://dx.doi.org/10.18273/revint.v35n1-2017001
Articulo
Original
Puntos
críticos y simetrías en problemas elípticos
Jaime Arango1
Juan Jiménez1,2
Andrés Salazar2∗
1Universidad del Valle,
Departamento de Matemáticas, Cali, Colombia.
2Universidad Javeriana Cali,
Departamento de Ciencias Naturales y Matemáticas, Cali, Colombia.
E-mail: andresmsalazar@javerianacali.edu.co
Resumen:
Se estima una cota superior para el número de puntos
críticos de la solución de un problema semilineal elíptico con condición de
Dirichlet nula en el borde de un dominio planar. El resultado se obtiene en
dominios simétricos con respecto a una recta y convexos en la dirección
ortogonal a la misma.
Palabras clave:
Principio del máximo, puntos críticos, componentes conexas, simetría.
Abstract:
In this paper we
estimate an upper bound for the number of critical points of the solution to a
semilinear elliptic problem with vanishing Dirichlet condition on a bounded
planar domain. The result is obtained assuming that the domain is symmetric
with respect to a line and convex in the orthogonal direction to the line of
symmetry.
Keywords: Maximum
principle, critical points, connected component, symmetry.
Recibido: 20 de septiembre
de 2016
Aceptado: 05 de abril de
2017,
Texto Completo disponible en PDF
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Para
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críticos y simetrías en problemas elípticos, Rev. Integr. Temas Mat. 35 (2017),
No. 1, 1–9.