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math.AP2025
Weighted nonlocal area functionals without the triangle inequality
Serena Dipierro, Enrico Valdinoci, Mary Vaughan
We consider a weighted nonlocal area functional in which the coefficients do not satisfy the triangle inequality. In the context of three phase transitions, this means that one of…
math.AP2024
A threshold for higher-order asymptotic development of genuinely nonlocal phase transition energies
Serena Dipierro, Enrico Valdinoci, Mary Vaughan
We study the higher-order asymptotic development of a nonlocal phase transition energy in bounded domains and with prescribed external boundary conditions. The energy under conside…
math.AP2024
Asymptotic expansion of a nonlocal phase transition energy
Serena Dipierro, Stefania Patrizi, Enrico Valdinoci +1
We study the asymptotic behavior of the fractional Allen--Cahn energy functional in bounded domains with prescribed Dirichlet boundary conditions. When the fractional power $s \in…