Annales Academiæ Scientiarum Fennicæ
Mathematica
Volumen 45, 2020, 279-292

BOUNDARY GROWTH OF SOBOLEV FUNCTIONS FOR DOUBLE PHASE FUNCTIONALS

Yoshihiro Mizuta and Tetsu Shimomura

4-13-11 Hachi-Hom-Matsu-Minami
Higashi-Hiroshima 739-0144, Japan; yomizuta 'at' hiroshima-u.ac.jp

Hiroshima University, Graduate School of Education, Department of Mathematics
Higashi-Hiroshima 739-8524, Japan; tshimo 'at' hiroshima-u.ac.jp

Abstract. We study growth properties of spherical means of Sobolev functions for the double phase functional Φ_p,q(x,t) = t^p + (b(x)t)^q in the unit ball B of Rⁿ, where 1 < p < q < ∞ and b(·) is a non-negative bounded function on B which is Hölder continuous of order θ ∈ (0,1].

2010 Mathematics Subject Classification: Primary 31B25, 31B15.

Key words: Sobolev functions, spherical mean, double phase functional.

Reference to this article: Y. Mizuta and T. Shimomura: Boundary growth of Sobolev functions for double phase functionals. Ann. Acad. Sci. Fenn. Math. 45 (2020), 279-292.

Full document as PDF file

https://doi.org/10.5186/aasfm.2020.4510