198 citations · 649 across the 125 of their papers we have counts for
13 papers · 2 filters
Improvement of flatness for nonlocal phase transitions
Serena Dipierro, Joaquim Serra, Enrico Valdinoci
We prove an improvement of flatness result for nonlocal phase transitions. For a class of nonlocal equations that includes , with~, we obtain a res…
Nonlocal phase transitions: rigidity results and anisotropic geometry
Serena Dipierro, Joaquim Serra, Enrico Valdinoci
We provide a series of rigidity results for a nonlocal phase transition equation. The prototype equation that we consider is of the form with~.…
A nonlinear free boundary problem with a self-driven Bernoulli condition
Serena Dipierro, Aram Karakhanyan, Enrico Valdinoci
We study a Bernoulli type free boundary problem with two phases $$J[u]=\int_Ω|\nabla u(x)|^2\,dx+Φ\big({\mathcal M}_-(u), {\mathcal{M}}_+(u)\big), \quad u-\bar u\in W^{1,2}_0(Ω), $…
Definition of fractional Laplacian for functions with polynomial growth\tha
Serena Dipierro, Ovidiu Savin, Enrico Valdinoci
We introduce a notion of fractional Laplacian for functions which grow more than linearly at infinity. In such case, the operator is not defined in the classical sense: nevertheles…
Asymptotic expansions of the contact angle in nonlocal capillarity problems
Serena Dipierro, Francesco Maggi, Enrico Valdinoci
We consider a family of nonlocal capillarity models, where surface tension is modeled by exploiting the family of fractional interaction kernels , with and…
Local approximation of arbitrary functions by solutions of nonlocal equations
Serena Dipierro, Ovidiu Savin, Enrico Valdinoci
We show that any function can be locally approximated by solutions of prescribed linear equations of nonlocal type. In particular, we show that every function is locally -calori…