On the well-posedness of global fully nonlinear first order elliptic systems
2018 ◽
Vol 7
(2)
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pp. 139-148
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AbstractIn the very recent paper [15], the second author proved that for any {f\in L^{2}(\mathbb{R}^{n},\mathbb{R}^{N})}, the fully nonlinear first order system {F(\,\cdot\,,\mathrm{D}u)=f} is well posed in the so-called J. L. Lions space and, moreover, the unique strong solution {u\colon\mathbb{R}^{n}\rightarrow\mathbb{R}^{N}} 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.
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2016 ◽
Vol 136
(5)
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pp. 676-682
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1978 ◽
Vol 43
(1)
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pp. 73-85
2003 ◽
Vol 3
(1)
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pp. 189-201
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2009 ◽
Vol 137
(10)
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pp. 3339-3350
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2010 ◽
Vol 2010
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pp. 1-39
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2015 ◽
Vol 53
(1)
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pp. 405-420
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