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

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arxiv 2412.09033 v1 pith:Z73WIBBK submitted 2024-12-12 math.AP

Daowen Lin , Xi-Nan Ma This is my paper · ORCID
classification math.AP
keywords bestclassconstantequationextremalfunctionshardy-sobolev-mazinequalities
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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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Cited by 2 Pith papers

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  1. Sharp gradient stability for a class of Hardy-Sobolev-Maz'ya inequalities

    math.AP 2025-08 conditional novelty 7.0 of 10

    For 3<=k<=n-1, 1<p<n, the deficit in the Hardy-Sobolev-Maz'ya inequality is bounded below by a constant times the gradient distance to the extremal manifold raised to the power max{2,p}, and this exponent is optimal.

  2. Radial symmetry and sharp asymptotic behaviors of nonnegative solutions to weighted doubly $D^{1,p}$-critical quasi-linear nonlocal elliptic equations with Hardy potential

    math.AP 2025-02 conditional novelty 6.0 of 10

    Every nontrivial nonnegative finite-energy weak solution of the doubly critical quasilinear Hartree equation with Hardy potential is radially symmetric and strictly decreasing, with sharp power-law asymptotics at the ...

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