5 papers
Long-range phase coexistence models with degenerate potentials
Francesco De Pas, Serena Dipierro, Enrico Valdinoci
This survey offers an overview of recent advances in nonlocal phase transition problems, modeled by Ginzburg--Landau type energies of the form \[ \frac{1}{4}\iint_{\R^{2n}\setminus…
Fredholm alternative for a general class of nonlocal operators
Francesco De Pas, Serena Dipierro, Enrico Valdinoci
We develop a Fredholm alternative for a fractional elliptic operator~ of mixed order built on the notion of fractional gradient. This operator constitutes the nonlocal…
Optimal decay of heteroclinic solutions of the fractional Allen-Cahn equation with a degenerate potential
Francesco De Pas, Serena Dipierro, Enrico Valdinoci
We refine the asymptotic estimates for minimizers of a class of nonlocal energy functionals of the form \[ \frac{1}{4} \iint_{\R^{2n} \setminus (\R^n \setminus Ω)^2} \snr{u(x) - u…
Reconstructing double-well potentials from transition layers in long-range phase coexistence models
Serena Dipierro, Francesco De Pas, Enrico Valdinoci
In models of phase coexistence, the precise form of the double-well potential is of central importance, yet it cannot be derived from first principles. In this paper, we investigat…
Heteroclinic connections for fractional Allen-Cahn equations with degenerate potentials
Francesco De Pas, Serena Dipierro, Mirco Piccinini +1
We investigate existence, uniqueness and asymptotic behavior of minimizers of a family of non-local energy functionals of the type $$ \frac{1}{4}\iint_{\mathbb{R}^{2n}\setminus (\m…