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3 papers
Extremals in Hardy-Littlewood-Sobolev inequalities for stable processes
Arturo de Pablo, Fernando Quirós, Antonella Ritorto
We prove the existence of an extremal function in the Hardy-Littlewood-Sobolev inequality for the energy associated to an stable operator. To this aim we obtain a concentration-com…
Regularity theory for singular nonlocal diffusion equations
Arturo de Pablo, Fernando Quirós, Ana Rodríguez
We prove continuity for bounded weak solutions of a nonlinear nonlocal parabolic type equation associated to a Dirichlet form with a rough kernel. The equation is allowed to be sin…
A general fractional porous medium equation
Arturo de Pablo, Fernando Quirós, Ana Rodríguez +1
We develop a theory of existence and uniqueness for the following porous medium equation with fractional diffusion, $$ \{ll} \dfrac{\partial u}{\partial t} + (-Δ)^{σ/2} (|u|^{m-1}u…