We deal with weighted Hardy–Sobolev type inequalities for functions on ℝd, d ≥ 2. The weights involved are anisotropic, given by products of powers of the distance to the origin and to a nontrivial subspace. We establish necessary and sufficient conditions for validity of these inequalities, and investigate the existence/nonexistence of extremal functions.
Hardy–Sobolev inequalities involving mixed radially and cylindrically symmetric weights
Musina R.
;
2026-01-01
Abstract
We deal with weighted Hardy–Sobolev type inequalities for functions on ℝd, d ≥ 2. The weights involved are anisotropic, given by products of powers of the distance to the origin and to a nontrivial subspace. We establish necessary and sufficient conditions for validity of these inequalities, and investigate the existence/nonexistence of extremal functions.File in questo prodotto:
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