Zobrazeno 1 - 10
of 180
pro vyhledávání: '"Teixeira, Eduardo V."'
We investigate a class of free boundary problems with oscillatory singularities within stochastic materials. Our main result yields sharp regularity estimates along the free boundary, provided the power of the singularity varies in a Dini-continuous
Externí odkaz:
http://arxiv.org/abs/2404.03060
Autor:
Snelson, Stanley, Teixeira, Eduardo V.
We consider a generalization of the Bernoulli free boundary problem where the underlying differential operator is a nonlocal, non-translation-invariant elliptic operator of order $2s\in (0,2)$. Because of the lack of translation invariance, the Caffa
Externí odkaz:
http://arxiv.org/abs/2403.11937
We establish higher regularity properties of solutions to fully nonlinear elliptic equations at interior critical points. The key novelty of our estimates lies in the fact that they yield smoothness properties that go beyond the inherent regularity l
Externí odkaz:
http://arxiv.org/abs/2312.02932
We prove that if $u\in C^0(B_1)$ satisfies $F(x,D^2u) \le 0$ in $B_1\subset \mathbb{R}^2$, in the viscosity sense, for some fully nonlinear $(\lambda, \Lambda)$-elliptic operator, then $u \in W^{2,\varepsilon}(B_{1/2})$, with appropriate estimates, f
Externí odkaz:
http://arxiv.org/abs/2212.03314
Autor:
Snelson, Stanley, Teixeira, Eduardo V.
We investigate Bernoulli free boundary problems prescribing infinite jump conditions. The mathematical set-up leads to the analysis of non-differentiable minimization problems of the form $\int \left(\nabla u\cdot (A(x)\nabla u) + \varphi(x) 1_{\{u>0
Externí odkaz:
http://arxiv.org/abs/2210.11494
Autor:
Snelson, Stanley, Teixeira, Eduardo V.
We prove the existence of an open set minimizing the first Dirichlet eigenvalue of an elliptic operator with bounded, measurable coefficients, over all open sets of a given measure. Our proof is based on a free boundary approach: we characterize the
Externí odkaz:
http://arxiv.org/abs/2209.10572
We prove that any solution of a degenerate elliptic PDE is of class $C^1$, provided the inverse of the equation's degeneracy law satisfies an integrability criterium, viz. $\sigma^{-1} \in L^1\left (\frac{1}{\lambda} {\bf d}\lambda\right )$. The proo
Externí odkaz:
http://arxiv.org/abs/2208.11016
We establish new quantitative Hessian integrability estimates for viscosity supersolutions of fully nonlinear elliptic operators. As a corollary, we show that the optimal Hessian power integrability $\varepsilon = \varepsilon(\lambda, \Lambda, n)$ in
Externí odkaz:
http://arxiv.org/abs/2204.06034
We prove higher-order fractional Sobolev regularity for fully nonlinear, uniformly elliptic equations in the presence of unbounded source terms. More precisely, we show the existence of a universal number $0< \varepsilon <1$, depending only on ellipt
Externí odkaz:
http://arxiv.org/abs/2204.03119
Publikováno v:
In Journal of Differential Equations 5 January 2025 414:890-903
