32 citations · 254 across the 68 of their papers we have counts for
8 papers · 1 filter
Rigidity of minimizers in nonlocal phase transitions
Ovidiu Savin
We obtain the classification of certain global bounded solutions for semilinear nonlocal equations of the type in ,with wher…
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…
Some remarks on the classification of global solutions with asymptotically flat level sets
Ovidiu Savin
We simplify some technical steps from \cite{S1} in which a conjecture of De Giorgi was addressed. For completeness we make the paper self-contained and reprove the classification o…
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…
Two-phase anisotropic free boundary problems and applications to the Bellman equation in 2D
Luis Caffarelli, Daniela De Silva, Ovidiu Savin
We prove Lipschitz continuity of solutions to a class of rather general two-phase anisotropic free boundary problems in 2D and we classify global solutions. As a consequence, we ob…
Global estimates for solutions to the linearized Monge--Ampère equations
Nam Q. Le, Truyen Nguyen
In this paper, we investigate regularity for solutions to the linearized Monge-Ampère equations when the nonhomogeneous term has low integrability. We establish global es…