Exact constant in Sobolev's and Sobolev's trace inequalities for Grand   Lebesgue Spaces with monomial weight
  We generalize in this article the classical Sobolev's and Sobolev's trace inequalities on the Grand Lebesgue Spaces under monomial weight instead the classical Lebesgue or grand Lebesgue Spaces.   We will distinguish the classical Sobolev's inequality and the so-called trace Sobolev's inequality. 
E. Ostrovsky, L. Sirota
math.FA