Hardy–Sobolev interpolation inequalities

We derive a family of interpolation estimates which improve Hardy’s inequality and cover the Sobolev critical exponent. We also determine all optimizers among radial functions in the endpoint case and discuss open questions on nonrestricted optimizers.

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Bibliographic Details
Published in:	Calculus of variations and partial differential equations Vol. 63; no. 7
Main Authors:	Dietze, Charlotte, Nam, Phan Thành
Format:	Journal Article
Language:	English
Published:	Berlin/Heidelberg Springer Berlin Heidelberg 01-09-2024 Springer Nature B.V
Subjects:	Analysis Calculus of Variations and Optimal Control; Optimization Control Interpolation Mathematical and Computational Physics Mathematics Mathematics and Statistics Systems Theory Theoretical 35Q55 35A23
Online Access:	Get full text
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Description
Summary:	We derive a family of interpolation estimates which improve Hardy’s inequality and cover the Sobolev critical exponent. We also determine all optimizers among radial functions in the endpoint case and discuss open questions on nonrestricted optimizers.
ISSN:	0944-2669 1432-0835
DOI:	10.1007/s00526-024-02800-x