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On the Boundary Harnack Principle for operators with different lower order terms
Daniela De Silva, Ovidiu Savin
We provide the classical Boundary Harnack principle in Lipschitz domains for solutions to two different linear uniformly elliptic equations with the same principal part.
Compactness estimates for minimizers of the Alt-Phillips functional of negative exponents
Daniela De Silva, Ovidiu Savin
We investigate the rigidity of global minimizers of the Alt-Phillips functional involving negative power potentials $$\int_Ω\left(|\nabla u|^2 + u^{-γ} χ_{\{u>0\}}\right)…
The Alt-Phillips functional for negative powers
Daniela De Silva, Ovidiu Savin
We develop the free boundary regularity for nonnegative minimizers of the Alt-Phillips functional for negative power potentials $$\int_Ω\left(\frac 1 2 |\nabla u|^2 + u^γ χ_{\{u>0\…
Quasi-Harnack inequality
Daniela De Silva, Ovidiu Savin
In this paper we obtain some extensions of the classical Krylov-Safonov Harnack inequality. The novelty is that we consider functions that do not necessarily satisfy an infinitesim…
Ressonant elliptic problems under Cerami condition
Edcarlos D. da Silva
We establish existence and multiplicity of solutions for a elliptic resonant elliptic problem under Dirichlet boundary conditions.