Fórmula de Gauss-Green sobre campos de medida divergente
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El presente trabajo extiende la fórmula de Gauss-Green a campos de medida divergente. Estos espacios fueron introducidos recientemente por Chen and Frid[1] para estudiar soluciones d´ebiles de cierto tipo de ecuaciones diferenciales parciales no lineales. Aplicando técnicas de teorÍa de la medida geométrica se estudiaran las propiedades de estos campos, en particular, resultados sobre densidad, la regla del producto, algunas caracterizaciones etc. Posteriormente se definirá la traza normal sobre subconjuntos con frontera Lipschitz deformable, como el límite débil de una sucesión de medidas de Radon, lo cual permitirá establecer la fórmula de Gauss-Green en campos de medida divergente.
Abstract. In this paper we extend the Gauss-Green formula to divergence-measure fields. These spaces were introduced recently by Chen and Frid[1] to study weak solutions of certain nonlinear partial differential equations. Applying techniques of geometric measure theory will study the properties of these fields, in particular, results on density, the product rule, some characterizations of these fields etc. Then define the normal traces over subsets with deformable Lipschitz boundaries, as the weak limit of a sequence of Radon measures, which will enable us to establish the Gauss-Green formula to divergence-measure fields.
Abstract. In this paper we extend the Gauss-Green formula to divergence-measure fields. These spaces were introduced recently by Chen and Frid[1] to study weak solutions of certain nonlinear partial differential equations. Applying techniques of geometric measure theory will study the properties of these fields, in particular, results on density, the product rule, some characterizations of these fields etc. Then define the normal traces over subsets with deformable Lipschitz boundaries, as the weak limit of a sequence of Radon measures, which will enable us to establish the Gauss-Green formula to divergence-measure fields.