Regularity Results for a Class of Functionals with Non-Standard Growth

✍ Scribed by Emilio Acerbi; Giuseppe Mingione

• Publisher: Springer
• Year: 2001
• Tongue: English
• Weight: 147 KB
• Volume: 156
• Category: Article
• ISSN: 0003-9527
• DOI: 10.1007/s002050100117

✦ Synopsis

We consider the integral functional f (x, Du) dx under non-standard growth assumptions that we call p(x) type: namely, we assume that |z| p(x) f (x, z) L(1 + |z| p(x) ), a relevant model case being the functional

Under sharp assumptions on the continuous function p(x) > 1 we prove regularity of minimizers. Energies exhibiting this growth appear in several models from mathematical physics.