3 papers
math.AP2026
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…
math.AP2026
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…
math.AP2026
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(…