Tohoku Mathematical Journal
2019
March
SECOND SERIES VOL. 71, NO. 1

Tohoku Math. J.
71 (2019), 53-68

Title RATIONAL ORBITS OF PRIMITIVE TRIVECTORS IN DIMENSION SIX

Author Fumi-Yuki Maeda, Takao Ohno and Tetsu Shimomura

(Received May 12, 2016, revised June 9, 2016)
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.

Mathematics Subject Classification. Primary 46E30; Secondary; 31B05.
Key words and phrases. Metric measure space, Newtonian space, Musielak-Orlicz space, Poincaré inequality, Dirichlet energy integral, obstacle problem, superminimizer.

To the top of this page

Back to the Contents