Articles liés à A Theory of Traces and the Divergence Theorem

A Theory of Traces and the Divergence Theorem - Couverture souple

Schuricht, Friedemann; Schönherr, Moritz

 
9783031866630: A Theory of Traces and the Divergence Theorem
Couverture souple
ISBN 10 : 3031866630 ISBN 13 : 9783031866630
Editeur : Springer, 2025

Synopsis

This book provides a new approach to traces, which are viewed as linear continuous functionals on some function space. A key role in the analysis is played by integrals related to finitely additive measures, which have not previously been considered in the literature. This leads to Gauss-Green formulas on arbitrary Borel sets for vector fields having divergence measure as well as for Sobolev and BV functions. The integrals used do not require trace functions or normal fields on the boundary and they can deal with inner boundaries. For the treatment of apparently intractable degenerate cases a second boundary integral is used. The calculus developed here also allows integral representations for the precise representative of an integrable function and for the usual boundary trace of Sobolev or BV functions. The theory presented gives a new perspective on traces for beginners as well as experts interested in partial differential equations. The integral calculus might also be a stimulating tool for geometric measure theory.

Les informations fournies dans la section « Synopsis » peuvent faire référence à une autre édition de ce titre.

À propos de l'auteur

Friedemann Schuricht is Professor of Mathematics at TU Dresden, Germany. His main research interests are in nonlinear analysis and its applications. In particular, he has worked on problems in the calculus of variations, partial differential equations, nonsmooth analysis, geometric analysis, and related applications in continuum mechanics.

Moritz Schönherr studied mathematics and completed his doctorate at TU Dresden, Germany. He has worked on problems in partial differential equations, measure theory and the foundations of continuum mechanics. Currently he has a business position in Copenhagen, Denmark.

Les informations fournies dans la section « A propos du livre » peuvent faire référence à une autre édition de ce titre.

Éditeur
Springer
Date d'édition
2025
Langue
anglais
ISBN 10 
3031866630
ISBN 13 
9783031866630
Reliure
Broché
Nombre de pages
188
Coordonnées du fabricant
Springer Nature Customer Service Center GmbH
ProductSafety@springernature.com

Europaplatz 3
Heidelberg
69115
Allemagne