4 citations · 19 across the 27 of their papers we have counts for
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Local Density of Solutions to Fractional Equations
Alessandro Carbotti, Serena Dipierro, Enrico Valdinoci
The study of nonlocal operators of fractional type possesses a long tradition, motivated both by mathematical curiosity and by real world applications...
The Fractional Malmheden Theorem
Serena Dipierro, Giovanni Giacomin, Enrico Valdinoci
We provide a fractional counterpart of the classical results by Schwarz and Malmheden on harmonic functions. From that we obtain a representation formula for -harmonic functions…
Nonlocal capillarity for anisotropic kernels
Alessandra De Luca, Serena Dipierro, Enrico Valdinoci
We study a nonlocal capillarity problem with interaction kernels that are possibly anisotropic and not necessarily invariant under scaling. In particular, the lack of scale invaria…
Integral operators defined "up to a polynomial''
Serena Dipierro, Aleksandr Dzhugan, Enrico Valdinoci
We introduce a suitable notion of integral operators (comprising the fractional Laplacian as a particular case) acting on functions with minimal requirements at infinity. For these…
A fractional glance to the theory of edge dislocations
Serena Dipierro, Stefania Patrizi, Enrico Valdinoci
We revisit some recents results inspired by the Peierls-Nabarro model on edge dislocations for crystals which rely on the fractional Laplace representation of the corresponding equ…
A Hong-Krahn-Szegö inequality for mixed local and nonlocal operators
Stefano Biagi, Serena Dipierro, Enrico Valdinoci +1
Given a bounded open set , we consider the eigenvalue problem of a nonlinear mixed local/nonlocal operator with vanishing conditions in the complement of…