Calculus of Variations and Geometric Measure Theory
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Divergence measure fields: generalizations of Gauss-Green formula

Giovanni Eugenio Comi (Scuola Normale Superiore)

created by comi on 14 Oct 2016

26 may 2016 -- 13:15   [open in google calendar]

Technische Universitaet Dresden (TUD) Mathematik AG Analysis & Stochastik

Abstract.

Divergence measure fields are $L^{p}$-summable vector fields whose divergence is a Radon measure. These new function spaces were introduced in the early 2000s by many authors for different purposes. Divergence measure fields provide a way to extend the Gauss-Green formula to the context of weakly differentiable vector fields and sets of finite perimeter. For my Master's thesis (written under the supervision of Prof. K. R. Payne), we explored especially the case $p = \infty$. Our method of proving the Gauss-Green formula for essentially bounded divergence-measure fields is different from the one of Chen, Torres and Ziemer, since we adapted the techniques already developed for BV functions in Vol'pert's work.


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