A Subelliptic Analogue of Aronson-Serrin's Harnack Inequality

Details A Subelliptic Analogue of Aronson-Serrin's Harnack Inequality A Subelliptic Analogue of Aronson-Serrin's Harnack Inequality

2011-09-21

arxiv.org/abs/1109.4596v1

Mathematics

Analysis of PDEs

Scientific paper

We show that the Harnack inequality for a class of degenerate parabolic quasilinear PDE $$\p_t u=X_i^* A_i(x,t,u,Xu)+ B(x,t,u,Xu),$$ associated to a system of Lipschitz continuous vector fields $X=(X_1,...,X_m)$ in in $\Om\times (0,T)$ with $\Om \subset M$ an open subset of a manifold $M$ with control metric $d$ corresponding to $X$ and a measure $d\sigma$ follows from the basic hypothesis of doubling condition and a weak Poincar\'e inequality. We also show that such hypothesis hold for a class of Riemannian metrics $g_\e$ collapsing to a sub-Riemannian metric $\lim_{\e\to 0} g_\e=g_0$ uniformly in the parameter $\e\ge 0$.

Affiliated with

Also associated with

No associations

Rating

A Subelliptic Analogue of Aronson-Serrin's Harnack Inequality 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 A Subelliptic Analogue of Aronson-Serrin's Harnack Inequality, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and A Subelliptic Analogue of Aronson-Serrin's Harnack Inequality will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-258118