Ovidiu Savin

most citedDensity estimates for a variational model driven by the Gagliardo norm

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math.AP2013

A localization theorem and boundary regularity for a class of degenerate Monge Ampere equations

Ovidiu Savin

We consider degenerate Monge-Ampere equations of the type $$\det D^2 u= f \quad \{in $\Om$}, \quad \quad f \sim \, d_{\p \Om}^α\quad \{near $\p \Om$,}$$ where $d_{\p \Om}$ represen…

math.AP2010★ 4 cited

Density estimates for a variational model driven by the Gagliardo norm

Ovidiu Savin, Enrico Valdinoci

We prove density estimates for level sets of minimizers of the energy $$\eps^{2s}\|u\|_{H^s(Ω)}^2+\int_ΩW(u)\,dx,$$ with $s \in (0, 1)$ , where $∥ u ∥_{H^{s} (Ω)}$ denotes the total con…

math.AP2010

$Γ$ -convergence for nonlocal phase transitions

Ovidiu Savin, Enrico Valdinoci

We discuss the $Γ$ -convergence, under the appropriate scaling, of the energy functional $∥ u ∥_{H^{s} (Ω)}^{2} + \int_{Ω} W (u) d x,$ with $s \in (0, 1)$ , where $∥ u ∥_{H^{s} (Ω)}$ denotes the t…

A localization theorem and boundary regularity for a class of degenerate Monge Ampere equations

Density estimates for a variational model driven by the Gagliardo norm

Γ-convergence for nonlocal phase transitions

$Γ$ -convergence for nonlocal phase transitions