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A theory of traces and the divergence theorem

Record Type:	Electronic resources : Monograph/item
Title/Author:	A theory of traces and the divergence theoremby Friedemann Schuricht, Moritz Schönherr.
Author:	Schuricht, Friedemann.
other author:	Schönherr, Moritz.
Published:	Cham :Springer Nature Switzerland :2025.
Description:	xiii, 174 p. :ill., digital ;24 cm.
Contained By:	Springer Nature eBook
Subject:	Calculus, Integral.
Online resource:	https://doi.org/10.1007/978-3-031-86664-7
ISBN:	9783031866647$q(electronic bk.)

A theory of traces and the divergence theorem
Schuricht, Friedemann.

A theory of traces and the divergence theorem[electronic resource] /by Friedemann Schuricht, Moritz Schönherr. - Cham :Springer Nature Switzerland :2025. - xiii, 174 p. :ill., digital ;24 cm. - Lecture notes in mathematics,v. 23721617-9692 ;. - Lecture notes in mathematics ;2035..

- 1. Introduction -- 2. Preliminaries About Measures -- 3. Theory of Traces -- 4. Divergence Theorems.

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.

ISBN: 9783031866647$q(electronic bk.)

Standard No.: 10.1007/978-3-031-86664-7doiSubjects--Topical Terms:

192542
Calculus, Integral.

LC Class. No.: QA308

Dewey Class. No.: 515.4

A theory of traces and the divergence theorem
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520 $a 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.
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