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arXiv · 2412.09033

Best constant and extremal functions for a class Hardy-Sobolev-Maz'ya inequalities

Daowen Lin·Xi-Nan Ma
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Abstract

We derive an integral identity for a class $p$-Laplace equation, and then classify all positive finite energy cylindrically symmetric solutions of the equation (\ref{1.2}) for $3\leq k\leq n-1,$ with the help of some a prior estimates. Combining this with the result of Secchi-Smets-Willem{\cite{SSW03}}, as a consequence, we obtain the best constant and extremal functions for the related Hardy-Sobolev-Maz'ya inequalities.

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Daowen Lin, Xi-Nan Ma. 2024-12-12. Best constant and extremal functions for a class Hardy-Sobolev-Maz'ya inequalities. https://arxiv.org/abs/2412.09033

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