Superficies Mínimas y Resultados de Separación en Variedades Riemannianas.: Dualidad y Aproximación en Espacios de Lebesgue Variable.
- Autores: Jesús Ocáriz Gallego
- Directores de la Tesis: Antonio Córdoba Barba (dir. tes.)
- Lectura: En la Universidad Autónoma de Madrid ( España ) en 2020
- Idioma: español
- Tribunal Calificador de la Tesis: Daniel Peralta Salas (presid.) , Fernando Chamizo Lorente (secret.) , David Cruz Uribe (voc.)
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- Resumen
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?
