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• W4362581906 abstract "The goal of this paper is to collect some known results on the monotonicity with respect to $p$ of the best constants associated with Sobolev immersions of type $W_0^{1,p}(Omega)hookrightarrow L^q(Omega)$ when $qin{1,p,infty}$. More precisely, letting $$lambda(p,q;Omega):=inflimits_{uin W_0^{1,p}(Omega) setminus{0}}{|;|nabla u|_D;|_{L^p(Omega)}}{|u|_{L^q(Omega)}^{-1}},,$$ we recall some monotonicity results related with the following functions begin{eqnarray*} (1,infty)ni p&mapsto &|Omega|^{p-1}lambda(p,1;Omega)^p,, (1,infty)ni p&mapsto &lambda(p,p;Omega)^p,, (D,infty)ni p&mapsto &lambda(p,infty;Omega)^p,, end{eqnarray*} when $Omegasubset mathbb{R}^{D}$ is a given open, bounded and convex set with smooth boundary." @default.
• W4362581906 created "2023-04-06" @default.
• W4362581906 creator A5046636896 @default.
• W4362581906 creator A5079358604 @default.
• W4362581906 date "2023-03-31" @default.
• W4362581906 modified "2023-10-18" @default.
• W4362581906 title "Monotonicity with respect to p of the best constants associated with Sobolev immersions of type $W_0^{1,p}(Omega)hookrightarrow L^q(Omega)$ when $qin{1,p,infty}$" @default.
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• W4362581906 doi "https://doi.org/10.24193/subbmath.2023.1.08" @default.
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