Zobrazeno 1 - 10
of 142
pro vyhledávání: '"De Silva, Daniela"'
We investigate a fully nonlinear two-phase free boundary problem with a Neumann boundary condition on the boundary of a general convex set $K \subset \mathbb{R}^n$ with corners. We show that the interior regularity theory developed by Caffarelli for
Externí odkaz:
http://arxiv.org/abs/2407.19538
Autor:
De Silva, Daniela, Savin, Ovidiu
We consider an energy model for harmonic graphs with junctions and study the regularity properties of minimizers and their free boundaries.
Externí odkaz:
http://arxiv.org/abs/2304.14203
Autor:
De Silva, Daniela, Savin, Ovidiu
We investigate the rigidity of global minimizers $u \ge 0$ of the Alt-Phillips functional involving negative power potentials $$\int_\Omega \left(|\nabla u|^2 + u^{-\gamma} \chi_{\{u>0\}}\right) \, dx, \quad \quad \gamma \in (0,2),$$ when the exponen
Externí odkaz:
http://arxiv.org/abs/2211.00553
We study vector-valued almost minimizers of the energy functional $$\int_D\left(|\nabla\mathbf{u}|^2+\frac2{1+q}\left(\lambda_+(x)|\mathbf{u}^+|^{q+1}+\lambda_-(x)|\mathbf{u}^-|^{q+1}\right)\right)dx,\quad0
Externí odkaz:
http://arxiv.org/abs/2207.06217
Autor:
De Silva, Daniela, Savin, Ovidiu
We obtain density estimates for the free boundaries of minimizers $u \ge 0$ of the Alt-Phillips functional involving negative power potentials $$\int_\Omega \left(|\nabla u|^2 + u^{-\gamma} \chi_{\{u>0\}}\right) \, dx, \quad \quad \gamma \in (0,2).$$
Externí odkaz:
http://arxiv.org/abs/2205.08436
Autor:
De Silva, Daniela, Savin, Ovidiu
We develop the free boundary regularity for nonnegative minimizers of the Alt-Phillips functional for negative power potentials $$\int_\Omega \left(\frac 1 2 |\nabla u|^2 + u^{\gamma} \chi_{\{u>0\}}\right) \, dx, \quad \quad \gamma \in (-2,0),$$ and
Externí odkaz:
http://arxiv.org/abs/2203.07123
In this paper we study vector-valued almost minimizers of the energy functional $$ \int_D\left(|\nabla\mathbf{u}|^2+2|\mathbf{u}|\right)\,dx . $$ We establish the regularity for both minimizers and the "regular" part of the free boundary. The analysi
Externí odkaz:
http://arxiv.org/abs/2112.00676
Given a global 1-homogeneous minimizer $U_0$ to the Alt-Caffarelli energy functional, with $sing(F(U_0)) = \{0\}$, we provide a foliation of the half-space $\R^{n} \times [0,+\infty)$ with dilations of graphs of global minimizers $\underline U \leq U
Externí odkaz:
http://arxiv.org/abs/2106.14576
Autor:
De Silva, Daniela, Savin, Ovidiu
We investigate the parabolic Boundary Harnack Principle for both divergence and non-divergence type operators by the analytical methods we developed in the elliptic context. Besides the classical case, we deal with less regular space-time domains, in
Externí odkaz:
http://arxiv.org/abs/2105.05692
Autor:
De Silva, Daniela, Tortone, Giorgio
We consider the vectorial analogue of the thin free boundary problem introduced in \cite{CRS} as a realization of a nonlocal version of the classical Bernoulli problem. We study optimal regularity, nondegeneracy, and density properties of local minim
Externí odkaz:
http://arxiv.org/abs/2010.05782