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On a variational principle for shape optimization and elliptic free boundary problems

  • González De Paz, Raúl B. [1]
    1. [1] Universidad del Valle de Guatemala

      Universidad del Valle de Guatemala

      Guatemala

  • Localización: Revista de Matemática: Teoría y Aplicaciones, ISSN 2215-3373, ISSN-e 2215-3373, Vol. 6, Nº. 1, 1999, págs. 67-84
  • Idioma: inglés
  • DOI: 10.15517/rmta.v6i1.169
  • Enlaces
  • Resumen
    • español

      Se presenta un principio variacional para varios problemas de valores en fronteras libres usando un enfoque de relajamiento. El funcional de Energía relajado es cóncavo y está definido en un conjunto convexo, de tal forma que los puntos que minimizan son funciones características de conjuntos. Como consecuencia de las condiciones de optimalidad de primer orden, se muestra que los conjuntos correspondientes son dominios acotados por fronteras libres, de manera que se prueba la equivalencia de la solución del problema relajado con la solución de varios problemas de valores en fronteras libres.Palabras claves: Cálculo de variaciones, optimización, problema de frontera libre.

    • English

      A variational principle for several free boundary value problems using a relaxation approach is presented. The relaxed Energy functional is concave and it is defined on a convex set, so that the minimizing points are characteristic functions of sets. As a consequence of the first order optimality conditions, it is shown that the corresponding sets are domains bounded by free boundaries, so that the equivalence of the solution of the relaxed problem with the solution of several free boundary value problem is proved.Keywords: Calculus of variations, optimization, free boundary problems.

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