On the continuity of solutions of the equations of a porous medium and the fast diffusion with weighted and singular lower-order terms

摘要

For the parabolic equation v(x)ut −  div (ω(x)um − 1 ∇ u) = f(x, t), u ≥ 0, m ≠ 1 we prove the continuity and the Harnack inequality for generalized k solutions, by using the weighted Riesz potential on the right-hand side of the equation.