Some Fractional Functional Inequalities and Applications to Some Constrained Minimization Problems Involving a Local Non-linearity

In this paper we prove the Fractional Gagliardo-Nirenberg Inequality, Polya-Szego Inequality and the Sharp Fractional Sobolev Inequality, we then provide an application of such inequalities in a constraiend variational problem involving the fractional gradient and alocal non-linearity