2017年12月

# Partial regularity for minimizers of a class of non autonomous functionals with nonstandard growth

CALCULUS OF VARIATIONS AND PARTIAL DIFFERENTIAL EQUATIONS
• Flavia Giannetti
• ,
• Antonia Passarelli di Napoli
• ,
• Maria Alessandra Ragusa
• ,
• Atsushi Tachikawa

56
6

Art. 153, 29

DOI
10.1007/s00526-017-1248-z

SPRINGER HEIDELBERG

We study the regularity of the local minimizers of non autonomous integral functionals of the type
integral(Omega) phi(p(x)) ((A(ij)(alpha beta)(x, u) D(i)u(alpha) D(i)u(beta))(1/2))dx,
where phi is an Orlicz function satisfying both the Delta(2) and the del(2) conditions, p(x) : Omega subset of R-n -&gt; (1, + infinity) is continuous and the function A(x, s) = (A(ij)(alpha beta) (x, s)) is uniformly continuous. More precisely, under suitable assumptions on the functions F and p(x), we prove the Holder continuity of the minimizers. Moreover, assuming in addition that the function A(x, s) = (A(ij)(alpha beta) (x, s)) is Holder continuous, we prove the partial Holder continuity of the gradient of the local minimizers too.

Web of Science ® 被引用回数 : 11

リンク情報
DOI
https://doi.org/10.1007/s00526-017-1248-z
Web of Science