198 citations · 649 across the 125 of their papers we have counts for
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A nonlocal free boundary problem
Serena Dipierro, Ovidiu Savin, Enrico Valdinoci
Given~ and a bounded domain~, we consider the following minimization problem of -Dirichlet plus -perimeter type $$ [u]_{ H^s(\R^{2n}\setminus(Ω^c)^…
Bifurcation results for a fractional elliptic equation with critical exponent in R^n
Serena Dipierro, Maria Medina, Ireneo Peral +1
In this paper we study some nonlinear elliptic equations in obtained as a perturbation of the problem with the fractional critical Sobolev exponent, that is $$ (-Δ)^s u = ε\…
Nonlocal problems with Neumann boundary conditions
Serena Dipierro, Xavier Ros-Oton, Enrico Valdinoci
We introduce a new Neumann problem for the fractional Laplacian arising from a simple probabilistic consideration, and we discuss the basic properties of this model. We can conside…
All functions are locally -harmonic up to a small error
Serena Dipierro, Ovidiu Savin, Enrico Valdinoci
We show that we can approximate every function with a -harmonic function in that vanishes outside a compact set. That is, -harmonic functions ar…
Concentration phenomena for the nonlocal Schrödinger equation with Dirichlet datum
Juan Davila, Manuel del Pino, Serena Dipierro +1
For a smooth, bounded domain , , we consider the nonlocal equation $$ ε^{2s} (-Δ)^s u+u=u^p \quad {\mbox{in}}Ω$$ with zero Dir…