Asymptotic behavior of least energy solutions of a biharmonic equation in dimension four Mohamed AyedMassimo GrossiKhalil Mehdi 35J6035J65biharmonic operatorleast energy solution In this paper we consider a biharmonic equation on a bounded domain in $\mathbb{R}^4$ with large exponent in the nonlinear term. We study asymptotic behavior of positive solutions obtained by minimizing suitable functionals. Among other results, we prove that $c_p$, the minimum of energy functional with the nonlinear exponent equal to $p$, is like $\rho_{4}e/p$ as $p \to +\infty$, where $\rho_{4} = 32\omega_{4}$ and $\omega_{4}$ is the area of the unit sphere $S^{3}$ in $\mathbb{R}^{4}$. Using this result, we compute the limit of the $L^{\infty}$-norm of least energy solutions as $p \to +\infty$. We also show that such solutions blow up at exactly one point which is a critical point of the Robin function. Indiana University Mathematics Journal 2006 text pdf 10.1512/iumj.2006.55.2723 10.1512/iumj.2006.55.2723 en Indiana Univ. Math. J. 55 (2006) 1723 - 1750 state-of-the-art mathematics http://iumj.org/access/