The purpose of these pages is to collect a set of notes that are a result of several talks and
minicourses delivered here and there in the world (Milan, Cortona, Pisa, Roma, Santiago del …

This paper deals with the fractional Sobolev spaces Ws, p. We analyze the relations among
some of their possible definitions and their role in the trace theory. We prove continuous and …

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arxiv:1307.1789v1 [math.AP] 6 Jul 2013 Page 1 arxiv:1307.1789v1 [math.AP] 6 Jul 2013 To
appear in Riv. Mat. Univ. Parma (NS) Giovanni Franzina and Giampiero Palatucci Fractional …

This paper focuses on the following scalar field equation involving a fractional Laplacian:(−)
αu= g (u) in RN, where N⩾ 2, α∈(0, 1),(−) α stands for the fractional Laplacian. Using some …

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Nonlinear equations for fractional Laplacians II: Existence, uniqueness, and qualitative
properties of solutions Page 1 TRANSACTIONS OF THE AMERICAN MATHEMATICAL …

This paper deals with the following class of nonlocal Schr\" odinger equations
$$\displaystyle (-\Delta)^ su+ u=| u|^{p-1} u\\\text {in}\\mathbb {R}^ N,\quad\text {for}\s\in (0 …

We prove some regularity estimates for viscosity solutions to a class of possible degenerate
and singular integro-differential equations whose leading operator switches between two …

The main goal of this work is to study existence, uniqueness and summability of the solution
u with respect to the summability of the datum f. In the process we establish an Lp-theory, for …