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June 2009 G-dense classes of elliptic equations in the plane
Gioconda Moscariello, Antonia Passarelli di Napoli, Carlo Sbordone
Funct. Approx. Comment. Math. 40(2): 283-295 (June 2009). DOI: 10.7169/facm/1246454031

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 $$H-\sqrt{H^2-1}\le \gamma_j(x)\le H+\sqrt{H^2-1}\,.$$

Citation

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Gioconda Moscariello. Antonia Passarelli di Napoli. Carlo Sbordone. "G-dense classes of elliptic equations in the plane." Funct. Approx. Comment. Math. 40 (2) 283 - 295, June 2009. https://doi.org/10.7169/facm/1246454031

Information

Published: June 2009
First available in Project Euclid: 1 July 2009

zbMATH: 1183.35024
MathSciNet: MR2543562
Digital Object Identifier: 10.7169/facm/1246454031

Subjects:
Primary: 35B27
Secondary: 30C62, 35F15

Rights: Copyright © 2009 Adam Mickiewicz University

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Vol.40 • No. 2 • June 2009
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