Calculus of Variations and Geometric Measure Theory
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G. Csato - B. Dacorogna - S. Sil

On the best constant in {G}affney inequality

created by csato on 12 Nov 2021

[BibTeX]

preprint

Inserted: 12 nov 2021

Year: 2017

ArXiv: 1712.04875 PDF

Abstract:

We discuss the value of the best constant in Gaffney inequality namely $$ \lVert \nabla \omega \rVert{L{2}}{2}\leq C\left( \lVert d\omega\rVert{L{2}}{2}+\lVert \delta\omega\rVert{L{2}% }{2}+\lVert \omega\rVert{L{2}}{2}\right) $$ when either $\nu\wedge\omega=0$ or $\nu\,\lrcorner\,\omega=0$ on $\partial\Omega.$

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