Geometric measure theory and the axioms of continuum thermodynamics
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.
scientific article; zbMATH DE number 3967979
scientific article