Sobolev's theorem for double phase functionals
Yoshihiro Mizuta, Takao Ohno, Tetsu Shimomura · Mathematical Inequalities & Applications · 2020
Our aim in this paper is to establish generalizations of Sobolev's theorem for double phase functionals (x,t) = t p + {b(x)t(log(e + t)) } q , where 1 0 and b is a nonnegative bounded function satisfying |b(x)b(y)| C|x -y| (log(e + |x -y| -1 )) - for 0 < 1 . Mathematics subject classification (2010)