198 citations · 649 across the 125 of their papers we have counts for
183 papers
Kernel representations of fractional gradient bilinear forms. Part I. Constant coefficients
Serena Dipierro, Caterina Sportelli, Enrico Valdinoci
We study the representation of bilinear forms associated with Riesz fractional gradients by symmetric integral kernels. Motivated by [SS18, Open Problem 1.10], we give a complete d…
On the Weyl tube formula for nonlocal perimeters
Serena Dipierro, Jack Thompson, Enrico Valdinoci
We study the asymptotic behaviour of the nonlocal perimeter of tubular neighbourhoods. For a closed submanifold of Euclidean space, we show that a suitable rescaling of t…
Boundedness of Solutions to Nonlocal Systems
Serena Dipierro, João Gonçalves da Silva, Giorgio Poggesi +1
Under mild mass or energy assumptions, we prove uniform bounds for all distributional solutions of a multi-dimensional system of nonlocal semilinear equations. The setti…
Dissolution and nucleation of jump discontinuities for one-dimensional periodic peridynamic waves
Giuseppe Maria Coclite, Serena Dipierro, Francesco Maddalena +2
We analyze solutions to a one-dimensional periodic linear model for peridynamic waves, focusing on the setting where the natural energy space allows for spatial discontinuities. Ex…
Asymptotics of nonlocal nonlinear Robin energies
Serena Dipierro, Giuseppe Spadaro, Enrico Valdinoci
We study the free minimization problem for a nonlinear, nonlocal functional associated with Robin-type nonlocal exterior conditions depending on a positive parameter . We prove…
A fractional critical problem in the halfspace with Neumann conditions
Azahara DelaTorre, Azahara DelaTorre Pedraza, Serena Dipierro +2
Given and , we construct nontrivial solutions of the problem \begin{equation*} \begin{cases} (-Δ)^s u=u^{2^*_s-1} &{\mbox{ in }}\mathbb{R}^n_+,\\ {\mathcal{N}}_s…