A General Theorem of Gau{\ss} Using Pure Measures

Autor:	Schönherr, Moritz, Schuricht, Friedemann
Rok vydání:	2017
Předmět:	Mathematics - Analysis of PDEs
Druh dokumentu:	Working Paper
Popis:	This paper shows that finitely additive measures occur naturally in very general Divergence Theorems. The main results are two such theorems. The first proves the existence of pure normal measures for sets of finite perime- ter, which yield a Gau{\ss} formula for essentially bounded vector fields having divergence measure. The second extends a result of Silhavy [19] on normal traces. In particular, it is shown that a Gau{\ss} Theorem for unbounded vector fields having divergence measure necessitates the use of pure measures acting on the gradient of the scalar field. All of these measures are shown to have their core on the boundary of the domain of integration. Comment: 46 pages, 2 figures
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/1710.02211 Zobrazit plný text záznamu View this record from Arxiv