• Existence of Solution of the Pullback Equation Involving Volume Forms

• # Fulltext

https://www.ias.ac.in/article/fulltext/pmsc/121/03/0339-0348

• # Keywords

Jacobian equation; pullback equation; volume forms.

• # Abstract

Let $\Omega\subset\mathbb{R}^n$ be a smooth, bounded domain. We study the existence and regularity of diffeomorphisms of 𝛺 satisfying the volume form equation

$$\phi^\ast(g)=f,\quad\text{in}\, \Omega$$

where $f,g\in C^{m,\alpha}(\overline{\Omega};\Lambda^n)$ are given positive volume forms.

• # Author Affiliations

1. Department of Mathematical Sciences, Indian Institute of Science Education and Research, Mohanpur Campus, P.O. BCKV Campus Main Office, Mohanpur 741 252, India

• # Proceedings – Mathematical Sciences

Current Issue
Volume 129 | Issue 3
June 2019