Exact constant in Sobolev's and Sobolev's trace inequalities for Grand Lebesgue Spaces with monomial weight

Abstract

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.