Geodesic
Boundary growth of Sobolev functions of monotone type for double phase functionals
Yoshihiro Mizuta1 ; Tetsu Shimomura2
1Hiroshima University, Graduate School of Advanced Science and Engineering, Department of Mathematics
2Hiroshima University, Graduate School of Humanities and Social Sciences, Department of Mathematics
Annales Fennici Mathematici, Tome 47 (2022) no. 1, pp. 23-37

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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 $\theta \in (0,1]$.
DOI : 10.54330/afm.112452
Keywords: Monotone Sobolev functions, spherical mean, double phase functional

Yoshihiro Mizuta  1   ; Tetsu Shimomura  2

1 Hiroshima University, Graduate School of Advanced Science and Engineering, Department of Mathematics
2 Hiroshima University, Graduate School of Humanities and Social Sciences, Department of Mathematics 
Yoshihiro Mizuta; Tetsu Shimomura. Boundary growth of Sobolev functions of monotone type for double phase functionals. Annales Fennici Mathematici, Tome 47 (2022) no. 1, pp. 23-37. doi: 10.54330/afm.112452
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