We study sign-changing viscosity solutions of the singularly perturbed fully nonlinear equation $$ F(D^2u_\varepsilon) = \frac{\alpha}{\varepsilon} \beta\left(\frac{u_\varepsilon}{\varepsilon}\right) \qquad\text{in }B_1\subset\mathbb R^n, $$ where $F$ is uniformly elliptic and $\beta\in C_c (-1,1)$ is nonnegative. We p...
Thialita M. Nascimento, Aelson Sobral, Eduardo V. Teixeira· 1 citation
We establish a general mechanism that turns qualitative smoothness into uniform, quantitative regularity estimates for fully nonlinear elliptic equations. The central conclusion is that, for compact classes preserved by the natural rescalings of the equation, qualitative and quantitative regularity have the same critic...
A classical consequence of Caffarelli's fully nonlinear regularity theory [L. A. Caffarelli, Ann. of Math. (2) 130 (1989), no. 1, 189-213] is that viscosity solutions of uniformly elliptic equations $F(D^2u)=f$, with $f\in L^p$, $p>n$, are locally $C^{1,\gamma}$ for every $\gamma<\min\{\alpha_H,\sigma_p\}$. Here $\alph...
Aelson Sobral, Eduardo V. Teixeira· 0 citations
We use cookies to run the site and, with your consent, for analytics and to show ads.
See our Cookie Policy.
