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 …

We consider nonuniformly elliptic variational problems and give optimal conditions
guaranteeing the local Lipschitz regularity of solutions in terms of the regularity of the given …

Local behavior of fractional p-minimizers - ScienceDirect Skip to main contentSkip to article
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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 …

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We investigate a class of quasi-linear nonlocal problems, including as a particular case semi-
linear problems involving the fractional Laplacian and arising in the framework of continuum …

One of the basic achievements in nonlinear potential theory is that the typical linear
pointwise estimates via fundamental solutions find a precise analog in the case of nonlinear …

Gradient estimates via non-linear potentials Page 1 Gradient estimates via non-linear
potentials Frank Duzaar, Giuseppe Mingione American Journal of Mathematics, Volume 133 …

We settle the longstanding problem of establishing pointwise potential estimates for vectorial
solutions u:→ RN to the non-homogeneous p-Laplacean system− div (| Du| p− 2 Du)= µ in⊂ …

We prove higher Hölder regularity for solutions of equations involving the fractional p-
Laplacian of order s, when p≥ 2 and 0< s< 1. In particular, we provide an explicit Hölder …