On the monotonicity of the best constant of Morrey’s inequality in convex domains

Fărcăşeanu, Maria; Mihăilescu, Mihai

doi:10.1090/proc/15826

On the monotonicity of the best constant of Morrey’s inequality in convex domains
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Proc. Amer. Math. Soc. 150 (2022), 651-660 Request permission

Abstract:

We investigate some monotonicity properties of the best constant from Morrey’s inequality in convex and bounded domains from the Euclidean space $\mathbb R^D$ ($D\geq 1$). Using these monotonicity properties we give a new variational characterization of the best constant from Morrey’s inequality on convex and bounded domains for which the maximum of the distance function to the boundary is small. We also show that this variational characterization does not hold true on convex and bounded domains for which the maximum of the distance function to the boundary is larger than $1$.

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