Nieto Roig, Juan JoséArea Carracedo, Iván CarlosDjida, Jean Daniel2019-07-112019-07-112019http://hdl.handle.net/10347/19116The value of integro-differentlal (non!oca!) operators to nonlinear differential equations is we!l-known. The combination of integro-differential operators and porous medium nonlinearities gives rise to interesting mathematical models that have been studied in the last decade both because of their mathematical properties and a number of scientific applications in different fields, such as engineering, physics, medicine and biology. ln this PhD Thesis, we are concerned with a number of nonlocal variants and extensions of nonlinear differential equations of porous medium-types, with suitable functional inequalities associated with the underlying functional spaces. We address several fundamenta! issues both linear and non!inear such as existence, uniqueness, boundary and interior regularity for nonnegative solutions. The De Giorgi-Nash-Moser HOider regularity techniques are used to prove continuity of solutions.engAttribution-NonCommercial-NoDerivatives 4.0 Internacionalhttp://creativecommons.org/licenses/by-nc-nd/4.0/Operadores non locaisProblemas de extensiónEcuacións en medio porosoMaterias::Investigación::12 Matemáticas::1202 Análisis y análisis funcional::120207 Ecuaciones en diferenciasMaterias::Investigación::12 Matemáticas::1202 Análisis y análisis funcional::120220 Ecuaciones diferenciales en derivadas parcialesdoctoral thesisopen access