Coarse-grained ellipticity and De Giorgi-Nash-Moser theory

Scott Armstrong, Benny Avelin, Cristiana De Filippis +2

We prove local boundedness and a Harnack inequality for nonnegative weak solutions of the equation $-\nabla \cdot (\mathbf{a}(x)\nabla u)=0$ under a coarse-grained ellipticity assump…