Differential and Integral Equations

On some nonlinear expressions of the Jacobian

Luigi Greco and Anna Verde

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Abstract

We define the expressions $J\log^{1+\alpha}(e+|D f|)$ and $J\log^{1+\alpha}(e+|J|)$ as Schwartz distributions, for $f\colon\Omega\subset{{\Bbb R}}^n\to {{\Bbb R}}^n$ a Sobolev mapping such that $|D f|^n\log^\alpha(e+|D f|)$ is locally integrable, $-1 <\alpha <0$, and $J$ the Jacobian determinant.

Article information

Source
Differential Integral Equations Volume 13, Number 10-12 (2000), 1569-1582.

Dates
First available in Project Euclid: 21 December 2012

Permanent link to this document
https://projecteuclid.org/euclid.die/1356061140

Mathematical Reviews number (MathSciNet)
MR1787082

Zentralblatt MATH identifier
0983.46034

Subjects
Primary: 46E30: Spaces of measurable functions (Lp-spaces, Orlicz spaces, Köthe function spaces, Lorentz spaces, rearrangement invariant spaces, ideal spaces, etc.)
Secondary: 47B38: Operators on function spaces (general)

Citation

Greco, Luigi; Verde, Anna. On some nonlinear expressions of the Jacobian. Differential Integral Equations 13 (2000), no. 10-12, 1569--1582. https://projecteuclid.org/euclid.die/1356061140.


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