Sharp regularity for the inhomogeneous porous medium equation

Damião J. Araújo, Anderson F. Maia, José Miguel Urbano

We show that locally bounded solutions of the inhomogeneous porous medium equation $$u_t-\mathrm{div}\left(m|u{|}^{m-1}\nabla u\right)=f\in L^{q,r},m>1,$$ are local…