Theory of traces and the divergence theorem / Friedemann Schuricht, Moritz Schönherr.

Format:

Book

Author/Creator:

Schuricht, Friedemann, author.

Schönherr, Moritz, author.

Series:

Lecture notes in mathematics (Springer-Verlag) ; no. 2372.

Lecture notes in mathematics, 0075-8434 ; 2372

Language:

English

Subjects (All):

Divergence theorem.

Function spaces.

Physical Description:

172 pages : illustrations (black and white) ; 24 cm

Place of Publication:

Cham, Switzerland : Springer, 2025.

Summary:

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.

Contents:

- 1. Introduction

2. Preliminaries About Measures

3. Theory of Traces

4. Divergence Theorems.

Notes:

Includes bibliographical references and index.

ISBN:

3031866630

9783031866630

OCLC:

1493489218

Publisher Number:

CIPO000250905