Resumen de Superficies Mínimas y Resultados de Separación en Variedades Riemannianas.: Dualidad y Aproximación en Espacios de Lebesgue Variable.
In this thesis, we solve four different problems of interdisciplinary nature using two different types of techniques: one of them concerning the analysis of partial differential equations and the other, functional analysis. More specifically, we address the following questions:
- What are the sufficient and necessary hypotheses so that a hypersurface is the set of discontinuities of a generalized harmonic function? - What are the geometric implications of achieving equality at Modica's estimate or its generalizations in Riemannian manifolds? - What is the dual of a variable Lebesgue space whose exponent function is unbounded? - Does the property of universal approximation of neural networks hold to approximate functions belonging to variable Lebesgue spaces?
