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 the Sobolev space H1,1(X,d,m) and of weak gradient with exponent 1. Eventually we apply these results to compare the area functional with the perimeter of the subgraph of f, in the same spirit as the classical theory.

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

AMBROSIO, Luigi;PINAMONTI, ANDREA;SPEIGHT, GARETH JAMES
2015

Abstract

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 the Sobolev space H1,1(X,d,m) and of weak gradient with exponent 1. Eventually we apply these results to compare the area functional with the perimeter of the subgraph of f, in the same spirit as the classical theory.
Settore MAT/05 - Analisi Matematica
Area formula; Metric measure spaces; Sobolev spaces; Tensorization;
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/11384/60322
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