• Existence of Solution of the Pullback Equation Involving Volume Forms

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      Permanent link:
      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

       

      Saugata Bandyopadhyay1

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

       
  • Proceedings – Mathematical Sciences | News

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