RT Dissertation/Thesis
T1 Some nonlocal operators in porous medium equations: the extension problem and regularity theory
A1 Djida, Jean Daniel
K1 Operadores non locais
K1 Problemas de extensión
K1 Ecuacións en medio poroso
AB The value of integro-differentlal (non!oca!) operators to nonlinear differential equations iswe!l-known. The combination of integro-differential operators and porous mediumnonlinearities gives rise to interesting mathematical models that have been studied in the lastdecade both because of their mathematical properties and a number of scientific applicationsin different fields, such as engineering, physics, medicine and biology. ln this PhD Thesis, weare concerned with a number of nonlocal variants and extensions of nonlinear differentialequations of porous medium-types, with suitable functional inequalities associated with theunderlying functional spaces. We address several fundamenta! issues both linear and non!inearsuch as existence, uniqueness, boundary and interior regularity for nonnegative solutions. TheDe Giorgi-Nash-Moser HOider regularity techniques are used to prove continuity of solutions.
YR 2019
FD 2019
LK http://hdl.handle.net/10347/19116
UL http://hdl.handle.net/10347/19116
LA eng
DS Minerva
RD 3 may 2026