A general regularity theorem for functionals with φ-growth

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:383

Article

Breit, Dominic²  Stroffolini, Bianca¹  Verde, Anna¹ 

[1] Univ Naples Federico 2, Dipartimento Matemat & Applicaz R Caccioppoli, I-80126 Naples, Italy

[2] Univ Saarland, D-66041 Saarbrucken, Germany

关键词: Vector-valued problems;    Local minimizers;    Nonstandard growth;    Regularity;   

DOI  :  10.1016/j.jmaa.2011.05.012

来源: Elsevier

【 摘 要 】

We prove C(1,alpha)-regularity for local minimizers of functionals integral(Omega)phi vertical bar del u vertical bar)dx, where phi is a Young function. In order to generalize the results of Fuchs (2011) [9] and Diening et al. (2009) [6], we assume for the function phi only the (Delta 2)-condition and phi ''(t) >= (epsilon) over cap phi'(t)/t for a positive constant (epsilon) over cap (and derivatives). of course a Holder-condition for the second (C) 2011 Elsevier Inc. All rights reserved.

【 授权许可】

Free