We describe the mathematical theory of diffusion and heat transport with a view to including
some of the main directions of recent research. The linear heat equation is the basic …

We construct a theory of existence, uniqueness and regularity of solutions for the fractional
heat equation∂ t u+(− Δ) su= 0, 0< s< 1, posed in the whole space RN with data in a class of …

We establish interior Schauder estimates for kinetic equations with integrodifferential
diffusion. We study equations of the form f t+ v⋅∇ xf= ℒ v f+ c, where ℒ v is an …

We establish sharp interior and boundary regularity estimates for solutions to∂ tu− L u= f (t,
x) in I× Ω, with I⊂ R and Ω⊂ R n. The operators L we consider are infinitesimal generators …

We study the regularity properties of the solutions to the nonlinear equation with fractional
diffusion,∂ tu+(−) σ/2 ϕ (u)= 0, for x∈ RN and t> 0, with 0< σ< 2 and N≥ 1. If the …

We study a parabolic equation for the fractional p-Laplacian of order s, for p≥ 2 and 0< s< 1.
We provide space-time Hölder estimates for weak solutions, with explicit exponents. The …

We prove space and time regularity for solutions of fully nonlinear parabolic integro-
differential equations with rough kernels. We consider parabolic equations u_t= I u ut= I u …

We study the positivity and regularity of solutions to the fractional porous medium equations
in for m> 1 and s∈(0, 1), with Dirichlet boundary data u= 0 in and nonnegative initial …

We study the regularity up to the boundary of solutions to fractional heat equation in
bounded C^ 1, 1 C 1, 1 domains. More precisely, we consider solutions to ∂ _t u+(-Δ)^ su …

In this article, we obtain higher Hölder regularity results for weak solutions to nonlocal
problems driven by the fractional double phase operator L u (x):= & 2\rm PV\mathbb R^ N| u …