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 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
URI	https://reading-clone.eprints-hosting.org/id/eprint/67058
Identification Number/DOI	10.1515/anona-2016-0049
Refereed	Yes
Divisions	Science > School of Mathematical, Physical and Computational Sciences > Department of Mathematics and Statistics
Publisher	Walter de Gruyter
Download/View statistics	View download statistics for this item