Continuity estimates for porous medium type equations with measure data

We consider parabolic equations of porous medium type of the form ut − divA(x, t, u,Du) = μ in ET , in some space time cylinderET . The most prominent example covered by our assumptions is the classical porous medium equation ut −∆u = μ in ET . We establish a sufficient condition for the continuity of u in terms of a natural Riesz potential of the right-hand side measure μ. As an application we come up with a borderline condition ensuring the continuity of u: more precisely, if μ ∈ L ( N+2 2 , 1 ) , then u is continuous in ET .