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arXiv · 2506.15611

Rigidity of solutions to singular/degenerate semilinear critical equations

Giovanni Catino·Dario Daniele Monticelli·Alberto Roncoroni
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Abstract

This paper deals with singular/degenerate semilinear critical equations which arise as the Euler-Lagrange equation of Caffarelli-Kohn-Nirenberg inequalities in $\mathbb{R}^d$, with $d\geq 2$. We prove several rigidity results for positive solutions, in particular we classify solutions with possibily infinite energy when the intrinsic dimension $n$ satisfies $2<n<4$.

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Giovanni Catino, Dario Daniele Monticelli, Alberto Roncoroni. 2025-06-18. Rigidity of solutions to singular/degenerate semilinear critical equations. https://arxiv.org/abs/2506.15611

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