Ti trovi qui: Home » News e Seminari

Divergence-measure fields and the Gauss-Green formulas

Martedì 8 maggio 2018, ore 12:00 in aula M1.8, edificio Matematica, Dipartimento FIM, Modena

Relatore: Dott. Giovanni Comi (Scuola Normale Superiore - Pisa)

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, and thus led to the definition of the divergence-measure fields. Such fields are L^p-summable vector fields on R^n, whose divergence is a Radon measure, and form a new family of function spaces, which in a sense generalize the BV fields. They were introduced at first by Anzellotti in 1983, and then they have been rediscovered in the early 2000s by many authors interested in various applications.
In this talk, we shall present an overview of such researches, with a particular focus on the results concerning the case p = ∞. In such case, Šilhavý (2005), Chen, Torres and Ziemer (2009) and Comi and Payne (2017) showed that Gauss–Green formulas hold for sets of finite perimeter and that the interior and exterior normal traces of the vector field are essentially bounded functions on the reduced boundary of the given set. Subsequent generalizations and applications will be also briefly discussed.

Ospiti: Prof. Gian Paolo Leonardi.

[Ultimo aggiornamento: 04/05/2018 10:08:33]