Tohoku Mathematical Journal

Obstacle problem for Musielak-Orlicz Dirichlet energy integral on metric measure spaces

Fumi-Yuki Maeda, Takao Ohno, and Tetsu Shimomura

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Abstract

We introduce Musielak-Orlicz Newtonian space on a metric measure space. After discussing properties of weak upper gradients of functions in such spaces and Poincaré inequalities for functions with zero boundary values in bounded open subsets, we prove the existence and uniqueness of a solution to an obstacle problem for Musielak-Orlicz Dirichlet energy integral.

Article information

Source
Tohoku Math. J. (2), Volume 71, Number 1 (2019), 53-68.

Dates
First available in Project Euclid: 9 March 2019

Permanent link to this document
https://projecteuclid.org/euclid.tmj/1552100442

Digital Object Identifier
doi:10.2748/tmj/1552100442

Mathematical Reviews number (MathSciNet)
MR3920790

Zentralblatt MATH identifier
07060326

Subjects
Primary: 46E30: Spaces of measurable functions (Lp-spaces, Orlicz spaces, Köthe function spaces, Lorentz spaces, rearrangement invariant spaces, ideal spaces, etc.)
Secondary: 31B05: Harmonic, subharmonic, superharmonic functions

Keywords
metric measure space Newtonian space Musielak-Orlicz space Poincaré inequality Dirichlet energy integral obstacle problem superminimizer

Citation

Maeda, Fumi-Yuki; Ohno, Takao; Shimomura, Tetsu. Obstacle problem for Musielak-Orlicz Dirichlet energy integral on metric measure spaces. Tohoku Math. J. (2) 71 (2019), no. 1, 53--68. doi:10.2748/tmj/1552100442. https://projecteuclid.org/euclid.tmj/1552100442


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