Calculus of Variations and Geometric Measure Theory

L. Ambrosio - A. Pinamonti - G. Speight

Tensorization of Cheeger energies, the space $H^{1,1}$ and the area formula for graphs

created by ambrosio on 13 Jul 2014
modified by speight on 16 May 2017


Published Paper

Inserted: 13 jul 2014
Last Updated: 16 may 2017

Journal: Advances in Mathematics
Volume: 281
Number: 1145-1177
Year: 2014


First we study in detail the tensorization properties of weak gradients in metric measure spaces $(X,d,m)$. Then, we compare potentially different notions of Sobolev space $H^{1,1}(X,d,m)$ and of weak gradient with exponent 1. Eventually we apply these results to compare the area functional $\int\sqrt{1+
\nabla f
_w^2}\,dm$ with the perimeter of the subgraph of $f$, in the same spirit as the classical theory.

Tags: GeMeThNES