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On the well-posedness of global fully nonlinear first order elliptic systems

Katzourakis, N. and Hussien, A. (2018) On the well-posedness of global fully nonlinear first order elliptic systems. Advances in Nonlinear Analysis, 7 (2). pp. 139-148. ISSN 2191-950X

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To link to this item DOI: 10.1515/anona-2016-0049

Abstract/Summary

In the very recent paper [15], the second author proved that for any f ∈ L2(ℝn,ℝN), the fully nonlinear first order system F(·, Du) = f is well posed in the so-called J. L. Lions space and, moreover, the unique strong solution u: ℝn → ℝN to the problem satisfies a quantitative estimate. A central ingredient in the proof was the introduction of an appropriate notion of ellipticity for F inspired by Campanato's classical work in the 2nd order case. Herein, we extend the results of [15] by introducing a new strictly weaker ellipticity condition and by proving well-posedness in the same “energy” space.

Item Type:Article
Refereed:Yes
Divisions:Faculty of Science > School of Mathematical, Physical and Computational Sciences > Department of Mathematics and Statistics
ID Code:67058
Publisher:Walter de Gruyter

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