We review what is known, unknown, and expected about the mathematical properties of
Coulomb and Riesz gases. Those describe infinite configurations of points in R d interacting …

In this paper we survey some results on the Dirichlet problem \left{_u=g^Lu=f_inR^n\Ω^inΩ\
right. for nonlocal operators of the form Lu\left(x\right)=PVR^n\left{u\left(x\right) …

Stochastic gradient descent (SGD) is one of the most popular algorithms in modern machine
learning. The noise encountered in these applications is different from that in many …

Progress in Mathematics is a series of books intended for professional mathematicians and
scientists, encompassing all areas of pure mathematics. This distinguished series, which …

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 study solutions to L u= f in Ω⊂ R n, being L the generator of any, possibly non-
symmetric, stable Lévy process. On the one hand, we study the regularity of solutions to L u …

We study the obstacle problem for integro-differential operators of order 2 s, with s ∈ (0, 1)
s∈(0, 1). Our main result establish that the free boundary is C^ 1, γ C 1, γ and u ∈ C^ 1 …

We deal with a class of equations driven by nonlocal, possibly degenerate, integro-
differential operators of differentiability order s∈(0, 1) and summability growth p∈(1,∞) …

We establish interior and up to the boundary Hölder regularity estimates for weak solutions
of the Dirichlet problem for the fractional g− Laplacian with bounded right hand side and g …

We present a simple discretization scheme for the hypersingular integral representa-tion of
the fractional Laplace operator and solver for the corresponding fractional Laplacian …