We show that locally bounded solutions of the inhomogeneous porous medium equation $$u_{ t} - { \rm div} \left( m |u|^{ m-1} \nabla u \right) = f \in L^{ q,r}, \quad m >1 ,$$ are locally H\"older continuous, with exponent $$\gamma =\min \left\{ \frac{ \alpha_{ 0}^-}{ m}, \frac{ [(2q - n)r -2q]}{ q[(mr - (m-1)]} \right\},$$ where $\alpha_{ 0}$ denotes the optimal H\"older exponent for solutions of the homogeneous case. The proof relies on an approximation lemma and geometric iteration in the appropriate intrinsic scaling.
Categories: math.AP