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  • Open Daily: 10am - 10pm
    Alley-side Pickup: 10am - 7pm

    3038 Hennepin Ave Minneapolis, MN
    612-822-4611

Open Daily: 10am - 10pm | Alley-side Pickup: 10am - 7pm
3038 Hennepin Ave Minneapolis, MN
612-822-4611
A Theory of Traces and the Divergence Theorem

A Theory of Traces and the Divergence Theorem

Schönherr, Moritz
Schuricht, Friedemann

Paperback

Series: Lecture Notes in Mathematics, Book 2372

General Mathematics

ISBN10: 3031866630
ISBN13: 9783031866630
Publisher: Springer
Published: Aug 12 2025
Pages: 174
Weight: 0.60
Height: 0.40 Width: 6.14 Depth: 9.21
Language: English
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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