Continuity of solutions to a nonlinear fractional diffusion equation

We study a parabolic equation for the fractional p-Laplacian of order s, for $$p\ge 2$$ p ≥ 2 and $$0<s<1$$ 0 < s < 1 . We provide space-time Hölder estimates for weak solutions, with explicit exponents. The proofs are based on iterated discrete differentiation of the equation in the spirit of Moser’s technique.

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

For the parabolic equation $$ \ v\left(x \right)u_{t} -{div({\omega(x)u^{m-1}}} \nabla u) = f(x,t)\: ,\; u\geq{0}\:,\; m\neq{1} $$ 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.

Continuity of solutions for the Δ ϕ -Laplacian operator

In this paper we give sufficient conditions to obtain continuity results of solutions for the so called ϕ-Laplacian Δ ϕ with respect to domain perturbations. We point out that this kind of results can be extended to a more general class of operators including, for instance, nonlocal nonstandard growth type operators.