Best constants in some exponential Sobolev inequalities Bernd KawohlMarcello Lucia 46E3535J60Schwarz symmetrizationMoser-Trudinger inequalityquasilinear equationsPohozaev identity A Pohozaev identity is used to classify the radial solutions of a quasilinear equation with exponential nonlinearity. The results are applied to find the infimum of the non-local functional \[ \mathcal{F}(\lambda,u)=\frac{1}{n}\int_{\Omega}|\nabla u|^n\,\mathrm{d}x-\lambda F\bigg(\barint{\Omega}e^u\,\mathrm{d}x\bigg),\quad u\in W^{1,n}_0(\Omega), \] for various nonlinearities $F$, where $\Omega$ is a bounded domain of $\mathbb{R}^n$ and $\lambda$ a real parameter. Our results generalize the case when $F(s)=\log s$. Indiana University Mathematics Journal 2008 text pdf 10.1512/iumj.2008.57.3307 10.1512/iumj.2008.57.3307 en Indiana Univ. Math. J. 57 (2008) 1907 - 1928 state-of-the-art mathematics http://iumj.org/access/