2015/09/17 by Alessia E. Kogoj, Kogoj, Alessia E., Sergio Polidoro +1
Mathematics · #Advanced Mathematical Physics Problems #Differential Equations and Boundary Problems #Spectral Theory in Mathematical Physics #math.AP
paper · pdf · doi:10.48550/arxiv.1509.05245
arxiv created 2015/09/17 · arxiv updated 2015/09/18
We consider nonnegative solutions u:Ω\longrightarrow ℝ of second order hypoelliptic equations \mathscrL u(x) =∑i,j=1n ∂xi (aij(x)∂xj u(x) ) + ∑i=1n bi(x) ∂xi u(x) =0, where Ω is a bounded open subset of ℝn and x denotes the point of Ω. For any fixed x0 ∈ Ω, we prove a Harnack inequality of this type supK u ≤ CK u(x0) ∀ u s.t. \mathscrL u=0, u≥ 0, where K is any compact subset of the interior of the \mathscrL-propagation set of x0 and the constant CK does not depend on u.