Calculus of Variations and Geometric Measure Theory

Z. Balogh - J. Manfredi - J. Tyson

Fundamental solution for the Q-Laplacian and sharp Moser-Trudinger inequality on Carnot groups

created on 23 Apr 2003
modified on 27 Apr 2004


Published Paper

Inserted: 23 apr 2003
Last Updated: 27 apr 2004

Journal: Journal of Functional Analysis
Volume: 204
Number: 1
Pages: 35-49
Year: 2003


For a general Carnot group $G$ with homogenous dimension $Q$ we prove the existence of a fundamental solution of the $Q$-Laplacian whose exponential is a homogenous norm on $G$. This implies a sharp version of the celebrated Moser-Trudinger inequality.

Keywords: Carnot group, Q-Laplacian , Fundamental solution, Moser-Trudinger inequality