Ovidiu Savin

Small Perturbation Solutions for Elliptic Equations

We consider viscosity solutions of fully nonlinear elliptic equations for which u ≡ 0 is a solution. We assume F is smooth and uniformly elliptic only in a neighborhood of the points (0, 0, 0, x), and show that u is smooth in the interior if ‖u‖ L ∞ is sufficiently small.

Pointwise ^{2,} estimates at the boundary for the Monge-Ampère equation

We obtain pointwise C estimates at boundary points for solutions to the Monge-Ampere equation under appropriate local conditions on the right hand side and boundary data.

Density Estimates for a Nonlocal Variational Model via the Sobolev Inequality

We consider the minimizers of the energy

Global ^{2,} estimates for the Monge-Ampère equation

\|u\|_{H^s(\Omega)}^2+\int_\Omega W(u)\,dx,

Some Singular Minimizers in Low Dimensions in the Calculus of Variations

with

A NONLOCAL FREE BOUNDARY PROBLEM

s \in (0,1/2)

Minimizers of convex functionals arising in random surfaces

, where

Regularity of Lipschitz free boundaries for the thin one-phase problem

\|u\|_{H^s(\Omega)}