Geometric measure theory and the axioms of continuum thermodynamics
type: Item
instance of: scholarly article
title: Geometric measure theory and the axioms of continuum thermodynamics
zbMATH Open document ID: 0599.73002
DOI: 10.1007/BF00250730
author: Morton E. Gurtin
author: W. O. Williams
author: William P. Ziemer
published in: Archive for Rational Mechanics and Analysis
publication date: 1986-01-01T00:00:00Z
review text: The paper is devoted to the problem of choosing an appropriate set description for the notion of a body which is basic to all of continuum physics. The usual choices, the standard domains of Whitney [\textit{H. Whitney}, Geometric integration theory (1957; Zbl 0083.282)] and the regular regions of Kellogg [\textit{O. D. Kellogg}, Foundations of potential theory (1967; Zbl 0152.313)], lead to inconsistencies in the axiomatic structure so that the authors propose a much broader class, the sets of finite perimeter, and demonstrate the viability of this measure-theoretic concept by using it to develop an axiomatic structure for continuum thermodynamics. For convenience, attention is restricted to rigid bodies. The techniques of geometric measure theory underlie the inference of the standard local forms of the first and second law of thermodynamics.
Mathematics Subject Classification ID: 74A15
Mathematics Subject Classification ID: 74Axx
Mathematics Subject Classification ID: 80A05
zbMATH DE Number: 3967979
zbMATH Keywords: Cacciappoli sets
zbMATH Keywords: sets of finite perimeter
zbMATH Keywords: measure-theoretic concept
Wikidata QID: Q114694841
reviewed by: Corneliu Ursescu
MaRDI profile type: Publication
cites work: Q3253193
cites work: Q5823489
cites work: Q5565773
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cites work: An axiomatic foundation for continuum thermodynamics
cites work: On internal interactions and the concept of thermal isolation
cites work: Thermodynamics of rigid continua
cites work: Q5817554
cites work: Approximately Continuous Transformations
cites work: Cauchy flux and sets of finite perimeter
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cites work: Q5334145
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description: scientific article; zbMATH DE number 3967979