Marcinkiewicz regularity for singular parabolic [formula omitted]-Laplace type equations with measure data

Abstract

We consider quasilinear parabolic equations with measurable coefficients when the right-hand side is a signed Radon measure with finite total mass, having p-Laplace type: ut−diva(Du,x,t)=μinΩ×(0,T)⊂Rn×R. In the singular range 2nn+1<p≤2−1n+1, we establish regularity estimates for the spatial gradient of solutions in the Marcinkiewicz spaces, under a suitable density condition of the right-hand side measure.