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This research monograph is motivated by problems in mathematical physics that involve
fractional kinetic equations. These equations describe transport dynamics in complex …

We study the fractional p-Laplace equation (− p) su= 0 for 0< s< 1 and in the subquadratic
case 1< p< 2. We provide Hölder estimates with an explicit Hölder exponent. The …

We prove Besov regularity estimates for the solution of the Dirichlet problem involving the
integral fractional Laplacian of order s in bounded Lipschitz domains Ω:‖ u‖ B˙ 2,∞ s+ r …

This paper describes the state of the art and gives a survey of the wide literature published
in the last years on the fractional Laplacian. We will first recall some definitions of this …

Abstract Very recently Warma (2019 SIAM J. Control Optim. to appear) has shown that for
nonlocal PDEs associated with the fractional Laplacian, the classical notion of controllability …

We study interior L p-regularity theory, also known as Calderon-Zygmund theory, of the
equation< L su, φ>:=∫ R n∫ R n K (x, y)(u (x)− u (y))(φ (x)− φ (y))| x− y| n+ 2 sdxdy=< f …

Page 1 Alessandro Carbotti, Serena Dipierro, and Enrico Valdinoci Local Density of Solutions
to Fractional Equations Page 2 De Gruyter Studies in Mathematics | Edited by Carsten …

This work is concerned with both higher integrability and differentiability for linear nonlocal
equations with possibly very irregular coefficients of VMO-type or even coefficients that are …

The integral fractional Laplacian of order s∈(0,1) is a nonlocal operator. It is known that
solutions to the Dirichlet problem involving such an operator exhibit an algebraic boundary …