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Existence of solution of the pullback equation involving volume forms

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Abstract

Let Ω ⊂ ℝn 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 \(f,g\in C^{m,\alpha}(\bar{\Omega};\Lambda^n)\) are given positive volume forms.

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

    SAUGATA BANDYOPADHYAY

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  1. SAUGATA BANDYOPADHYAY
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BANDYOPADHYAY, S. Existence of solution of the pullback equation involving volume forms. Proc Math Sci 121, 339–348 (2011). https://doi.org/10.1007/s12044-011-0032-9

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