Extremal functions for Adams' inequalities in dimension four

Xiaomeng Li

Let $\Omega \subset {\mathbb{R}}^4$ be a smooth bounded domain, $W_0^{2,2}(\Omega )$ be the usual Sobolev space. For any positive integer $\ell$, ${\lambda }_{\ell }(\Omega )$ is the $\ell$-th eigenvalue of the…