Calculus of Variations and Geometric Measure Theory
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The Gauss-Green theorem in stratified groups

Giovanni Eugenio Comi (Scuola Normale Superiore)

created by comi on 28 Feb 2018
modified on 02 May 2018

27 feb 2018 -- 14:30   [open in google calendar]

Dipartimento di Matematica e Informatica, Ferrara.

Abstract.

The Gauss--Green formulas are of significant relevance in many areas of mathematical analysis and mathematical physics. This motivated several investigations to extend such formulas to more general classes of integration domains and weakly differentiable vector fields. In the Euclidean setting it has been shown by Silhavy (2005) and Chen, Torres and Ziemer (2009) that Gauss-Green formulas hold for sets of finite perimeter and $L^{\infty}$-divergence measure fields, i. e. essentially bounded vector fields whose distributional divergence is a Radon measure. We extend these results to the context of stratified groups. In particular, we prove the existence of generalized normal traces on the reduced boundary of sets of locally finite h-perimeter without requiring De Giorgi's rectifiability theorem to hold. This is a joint work with V. Magnani.


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