Continuity Properties of Minimizers of Integral Functionals in a Limit Case

✍ Scribed by Vincenzo Ferone; Nicola Fusco

• Publisher: Elsevier Science
• Year: 1996
• Tongue: English
• Weight: 241 KB
• Volume: 202
• Category: Article
• ISSN: 0022-247X
• DOI: 10.1006/jmaa.1996.0301

✦ Synopsis

We prove continuity of minimizers of integral functionals of the form w Ž .

x Ž . < < p H f x, u, Du q hDu , where the integrand f x,, grows like , with ⍀ 0 0 p ) 1, and h is in a suitable Lorentz space. Continuity of solutions of nonlinear Ž . Ž . equations of the form div A x, u, Du s div h is also proved, where A x, , < < py1 grows like .