Lower Semicontinuity of Functionals via the Concentration-Compactness Principle

✍ Scribed by Eugenio Montefusco

• Publisher: Elsevier Science
• Year: 2001
• Tongue: English
• Weight: 108 KB
• Volume: 263
• Category: Article
• ISSN: 0022-247X
• DOI: 10.1006/jmaa.2001.7631

✦ Synopsis

In this paper we show the weak lower semicontinuity of some classes of functionals, using the concentration-compactness principle of P. L. Lions. These functionals involve an integral term, and we do not know whether it can be handled by the De Giorgi theorem. The semicontinuity result allows us to prove several existence results for quasilinear elliptic equations.