Lipschitz continuity of solutions of Poisson equations in metric measure spaces

Details Lipschitz continuity of solutions of Poisson equations in metric measure spaces Lipschitz continuity of solutions of Poisson equations in metric measure spaces

2010-04-07

arxiv.org/abs/1004.1101v3

Mathematics

Analysis of PDEs

Potential Analysis, to appear

Scientific paper

Let $(X,d)$ be a pathwise connected metric space equipped with an Ahlfors $Q$-regular measure $\mu$, $Q\in[1,\infty)$. Suppose that $(X,d,\mu)$ supports a 2-Poincar\'e inequality and a Sobolev-Poincar\'e type inequality for the corresponding "Gaussian measure". The author uses the heat equation to study the Lipschitz regularity of solutions of the Poisson equation $\Delta u=f$, where $f\in L^p_\loc$. When $p>Q$, the local Lipschitz continuity of $u$ is established.

Affiliated with

Also associated with

No associations

Rating

Lipschitz continuity of solutions of Poisson equations in metric measure spaces does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Lipschitz continuity of solutions of Poisson equations in metric measure spaces, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Lipschitz continuity of solutions of Poisson equations in metric measure spaces will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-397613