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

Daowen Lin; Xi-Nan Ma

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

Analysis of PDEs 2024-12-13 v1

Authors: Daowen Lin , Xi-Nan Ma

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.

Keywords

Hardy-Sobolev-Maz'ya inequality best constant extremal functions p-Laplace equation cylindrical symmetry

Cite

@article{arxiv.2412.09033,
  title  = {Best constant and extremal functions for a class Hardy-Sobolev-Maz'ya inequalities},
  author = {Daowen Lin and Xi-Nan Ma},
  journal= {arXiv preprint arXiv:2412.09033},
  year   = {2024}
}

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20 pages

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