Functiones et Approximatio Commentarii Mathematici

G-dense classes of elliptic equations in the plane

Gioconda Moscariello, Antonia Passarelli di Napoli, and Carlo Sbordone

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Abstract

We show that, for $\Omega$ a bounded convex domain of $\mathbb{R}^2$, any $2\times 2$ symmetric matrix $A(x)$ with $\det A(x)=1$ for a.e. $x\in\Omega$ satisfying the ellipticity bounds $$\frac{|\xi|^2}{H}\le \langle A(x)\xi,\xi\rangle \le H|\xi|^2$$ for a.e. $x\in\Omega$ and for all $\xi\in\mathbb{R}^2$ can be approximated, in the sense of $G$-convergence, by a sequence of matrices of the type $$\left(\begin{matrix}\gamma_j(x)& 0\\ 0&\frac{1}{\gamma_j(x)}\end{matrix}\right)$$ with $$H-\sqrt{H^2-1}\le \gamma_j(x)\le H+\sqrt{H^2-1}\,.$$

Article information

Source
Funct. Approx. Comment. Math., Volume 40, Number 2 (2009), 283-295.

Dates
First available in Project Euclid: 1 July 2009

Permanent link to this document
https://projecteuclid.org/euclid.facm/1246454031

Digital Object Identifier
doi:10.7169/facm/1246454031

Mathematical Reviews number (MathSciNet)
MR2543562

Zentralblatt MATH identifier
1183.35024

Subjects
Primary: 35B27: Homogenization; equations in media with periodic structure [See also 74Qxx, 76M50]
Secondary: 35F15: Boundary value problems for linear first-order equations 30C62: Quasiconformal mappings in the plane

Keywords
G-convergence quasiconformal maps

Citation

Moscariello, Gioconda; Passarelli di Napoli, Antonia; Sbordone, Carlo. G-dense classes of elliptic equations in the plane. Funct. Approx. Comment. Math. 40 (2009), no. 2, 283--295. doi:10.7169/facm/1246454031. https://projecteuclid.org/euclid.facm/1246454031


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