This analysis reveals rigidity for positive solutions to degenerate semilinear equations, suggesting classification strategies for singular cases.
This paper deals with singular/degenerate semilinear critical equations which arise as the Euler-Lagrange equation of Caffarelli-Kohn-Nirenberg inequalities in Rᵈ, with d≥ 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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Catino et al. (2025) studied this question.
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