Geodesic
Boundary growth of Sobolev functions of monotone type for double phase functionals
Yoshihiro Mizuta1 ; Tetsu Shimomura2
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
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 
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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. http://geodesic.mathdoc.fr/articles/10.54330/afm.112452/

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