Elliptic and Parabolic Equations - Abstract

Liskevich, Vitali A.

Qualitative properties of solutions to second-order elliptic and parabolic equations with lower order coefficients

In this talk we will discuss recent result on basic properties of solutions to divergence type second-order elliptic and parabolic equations with lower order coefficients from Kato classes. Amongst the properties are local boundedness, continuity, Harnack inequality and removability of singularities. New pointwise estimates of solutions to parabolic equations via Wolff potentials will be given. Corresponding results for linear equations will be also surveyed.