Oberseminar Mathematik in den Naturwissenschaften "Regularity for nonuniformly elliptic equations"

I will discuss regularity properties for solutions of linear non-uniformly elliptic equations in divergence form. Assuming certain integrability conditions on the coefficient field, we obtain local boundedness and validity of Harnack inequality. The assumed integrability assumptions are essentially sharp and improve upon some classical results in the literature.

Further, I discuss applications to optimal regularity estimates for linear uniformly elliptic equations and certain nonlinear nonuniformly equations.