A Necas-Lions inequality with symmetric gradients on star-shaped domains based on a first order Babuska-Aziz inequality

Keywords

Advanced Numerical Methods for Scientific Computing
Code:
52/2024
Title:
A Necas-Lions inequality with symmetric gradients on star-shaped domains based on a first order Babuska-Aziz inequality
Date:
Friday 2nd August 2024
Author(s):
Botti, M.; Mascotto, L.
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Abstract:
We prove a Necas-Lions inequality with symmetric gradients on two and three dimensional domains that are star-shaped with respect to a ball B; the constants in the inequality are explicit with respect to the diameter and the radius of B. Crucial tools in deriving this inequality are a first order Babuska-Aziz inequality based on Bogovskii's construction of a right-inverse of the divergence and Fourier transform techniques proposed by Duran. As a byproduct, we derive arbitrary order estimates in arbitrary dimension for that operator.
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