Speaker: Thialita M. Nascimento from University of Central Florida
Abstract: In this talk, we will discuss new universal bounds for the exponent of Hessian integrability of viscosity supersolutions of fully nonlinear and uniformly elliptic equations, by means of geometric and measure theoretic arguments. Such estimates produce a quantitative improvement in the decay of this exponent with respect to dimension. In particular, we solve, in the negative, the Armstrong-Silvestre-Smart Conjecture about the optimal exponent for the Hessian integrability. This is a joint work with Prof. Eduardo Teixeira (UCF-USA).