On distributional adjugate and derivative of the inverse

Authors

  • Stanislav Hencl Charles University, Department of Mathematical Analysis
  • Aapo Kauranen Universitat Autònoma de Barcelona, Departament de Matemàtiques
  • Jan Malý Charles University, Department of Mathematical Analysis

Keywords:

bounded variation, distributional Jacobian

Abstract

Let ΩR3 be a domain and let f:ΩR3 be a bi-BV homeomorphism. Very recently in [16] it was shown that the distributional adjugate of Df (and thus also of Df1) is a matrix-valued measure. In the present paper we show that the components of Adj Df coincide with the components of Df1(f(U)) as measures and that the absolutely continuous part of the distributional adjugate Adj Df equals to the pointwise adjugate adj Df(x) a.e. We also show the equivalence of several approaches to the definition of the distributional adjugate.

 

Section
Articles

Published

2021-06-21

How to Cite

Hencl, S., Kauranen, A., & Malý, J. (2021). On distributional adjugate and derivative of the inverse. Annales Fennici Mathematici, 46(1), 21–42. Retrieved from https://afm.journal.fi/article/view/109342