On the optimal domain for minimizing the buckling load of a clamped plate

Abstract: We prove the existence of an optimal domain for minimizing the buckling load among all, possibly unbounded, open subsets of $\mathbb{R}^n$ ($n\geq 2$) with given measure. Our approach is based on the extension of a 2-dimensional existence result of Ashbaugh and Bucur and on the idea of Alt and Caffarelli to focus on the eigenfunction.