Open AccessBoundary growth of Sobolev functions of monotone type for double phase functionals
Author(s) -
Yoshihiro Mizuta,
Tetsu Shimomura
Publication year - 2021
Publication title -
annales fennici mathematici
Language(s) - English
Resource type - Journals
eISSN - 2737-114X
pISSN - 2737-0690
DOI - 10.54330/afm.112452
Subject(s) - sobolev space , monotone polygon , mathematics , unit sphere , bounded function , boundary (topology) , ball (mathematics) , type (biology) , mathematical analysis , function (biology) , order (exchange) , combinatorics , pure mathematics , geometry , ecology , evolutionary biology , biology , finance , economics
Our aim in this paper is to deal with boundary growth of spherical means of Sobolev functions of monotone type for the double phase functional \(\Phi_{p,q}(x,t) = t^{p} + (b(x) t)^{q}\) in the unit ball B of \(\mathbb{R}^n\), where \(1 < p < q < \infty\) and \(b(\cdot)\) is a non-negative bounded function on B which is Hölder continuous of order \(\theta \in (0,1]\).