Abstract
From the Hardy and Sobolev inequalities
where \(\delta (\mathbf{x}) =\mathrm{ dist}(\mathbf{x},\partial \Omega ),C_{H},C_{S}\) are the optimal constants and p ∗ = np∕(n − p), it follows that for 0 < α ≤ C H ,
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Balinsky, A.A., Evans, W.D., Lewis, R.T. (2015). Hardy, Sobolev, Maz’ya (HSM) Inequalities. In: The Analysis and Geometry of Hardy's Inequality. Universitext. Springer, Cham. https://doi.org/10.1007/978-3-319-22870-9_4
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DOI: https://doi.org/10.1007/978-3-319-22870-9_4
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-22869-3
Online ISBN: 978-3-319-22870-9
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