Regularity results for a class of functionals with non-standard growth

Authors
Acerbi, E Mingione, G
Citation
E. Acerbi et G. Mingione, Regularity results for a class of functionals with non-standard growth, ARCH R MECH, 156(2), 2001, pp. 121-140
Citations number
34
Categorie Soggetti
Mathematics,"Mechanical Engineering
Journal title
ARCHIVE FOR RATIONAL MECHANICS AND ANALYSIS
ISSN journal
00039527 → ACNP
Volume
156
Issue
2
Year of publication
2001
Pages
121 - 140
Database
ISI
SICI code
0003-9527(2001)156:2<121:RRFACO>2.0.ZU;2-0
Abstract
We consider the integral functional integral f(x, Du) dx under non-standard growth assumptions that we call p(x) type: namely, we as sume that \z\(p(x)) less than or equal to f (x, z) less than or equal to L (1 + \z\(p (x))), a relevant model case being the functional integral \Du\(p(x)) dx. Under sharp assumptions on the continuous function p(x) > 1 we prove regula rity of minimizers. Energies exhibiting this growth appear in several model s from mathematical physics.