An example of a functional which is weakly lower semicontinuous on \(W_0^{1,p}\) for every \(p>2\) but not on \(H_0^1\)

DOI10.4171/ZAA/1423zbMath1211.49015OpenAlexW2058339502MaRDI QIDQ628815

Fernando Farroni, François Murat, Raffaella Giova

Publication date: 7 March 2011

Published in: Zeitschrift für Analysis und ihre Anwendungen (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.4171/zaa/1423

zbMATH Keywords

lower semicontinuityHardy-Sobolev inequalities

Mathematics Subject Classification ID

Methods involving semicontinuity and convergence; relaxation (49J45) Inequalities involving derivatives and differential and integral operators (26D10)

Related Items (1)

Existence theorems of nontrivial and positive solutions for nonlocal inhomogeneous elliptic problems

Cites Work

• Unnamed Item
• An introduction to Sobolev spaces and interpolation spaces
• A unified approach to improved $L^p$ Hardy inequalities with best constants
• Semicontinuity problems in the calculus of variations
• Direct methods in the calculus of variations

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