On a Hardy–Morrey inequality
Artikel i vetenskaplig tidskrift, 2025

Morrey's classical inequality implies the Hölder continuity of a function whose gradient is sufficiently integrable. Another consequence is the Hardy-type inequality [Formula presented] for any open set Ω⊊Rn. This inequality is valid for functions supported in Ω and with λ a positive constant independent of u. The crucial hypothesis is that the exponent p exceeds the dimension n. This paper aims to develop a basic theory for this inequality and the associated variational problem. In particular, we study the relationship between the geometry of Ω, sharp constants, and the existence of a nontrivial u which saturates the inequality.

Sharp constants

Sobolev inequalities

Extremals

Författare

Ryan Hynd

University of Pennsylvania

Simon Larson

Chalmers, Matematiska vetenskaper, Analys och sannolikhetsteori

Göteborgs universitet

Erik Lindgren

Kungliga Tekniska Högskolan (KTH)

Journal of Functional Analysis

0022-1236 (ISSN) 1096-0783 (eISSN)

Vol. 289 6 111002

Ämneskategorier (SSIF 2025)

Matematisk analys

DOI

10.1016/j.jfa.2025.111002

Mer information

Senast uppdaterat

2025-05-09