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We prove a reverse-Holder inequality for functions $u$ realizing the best constant in the Sobolev inequality, that is\n  $$\\mathcal{C}_p(\\Omega) = \\inf \\left \\{ \\frac{\\int_\\Omega |\\nabla v|^2}{\\left ( \\int_\\Omega |v|^p \\right )^{2/p}} \\right \\} = \\frac{\\int_\\Omega |\\nabla u|^2}{\\left ( \\int_\\Omega |u|^p \\right )^{2/p}}.$$\n  Our inequality has the form $\\| u \\|_{L^p} \\geq K \\| u \\|_{L^q}$ for any $q > p$, where $K$ depends only on $n$, $p$, $q$, and $\\mathcal{C}_p(\\Omega)$. 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We prove a reverse-Holder inequality for functions $u$ realizing the best constant in the Sobolev inequality, that is\n  $$\\mathcal{C}_p(\\Omega) = \\inf \\left \\{ \\frac{\\int_\\Omega |\\nabla v|^2}{\\left ( \\int_\\Omega |v|^p \\right )^{2/p}} \\right \\} = \\frac{\\int_\\Omega |\\nabla u|^2}{\\left ( \\int_\\Omega |u|^p \\right )^{2/p}}.$$\n  Our inequality has the form $\\| u \\|_{L^p} \\geq K \\| u \\|_{L^q}$ for any $q > p$, where $K$ depends only on $n$, $p$, $q$, and $\\mathcal{C}_p(\\Omega)$. 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