Boundary growth of Sobolev functions of monotone type for double phase functionals
Yoshihiro Mizuta, Tetsu Shimomura · Annales Fennici Mathematici · 2021
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 \(\theta \in (0,1]\).