Adams-Onofri Inequality with Logarithmic Weight and the Associated Mean Field Bi-Harmonic Equation

Abstract

This paper is devoted to establishing the Adams-Onofri inequality with logarithmic weight for the second order radial Sobolev space defined on the unit ball in $\mathbb{R}^4.$ By using this inequality we obtain the existence of solutions for mean field biharmonic equation with logarithmic weight.