2016/10/11 by Aimar, Hugo, Beltritti, Gastón, Gómez, Ivana +1
#Analysis of PDEs (math.AP) #FOS: Mathematics
paper · doi:10.48550/arxiv.1610.03206
We obtain a new general extension theorem in Banach spaces for operators which are not required to be symmetric, and apply it to obtain Harnack estimates and a priori regularity for solutions of fractional powers of several second order differential operators. These include weighted elliptic and subellitptic operators in divergence form (nonnecessarily self-adjoint), and nondivergence form operators with rough coefficients. We utilize the reflection extension technique introduced by Caffarelli and Silvestre.