On the optimal domain for minimizing the buckling load of a clamped plate
Kathrin Stollenwerk · Zeitschrift für angewandte Mathematik und Physik · 2022
Abstract We prove the existence of an optimal domain for minimizing the buckling load among all, possibly unbounded, open subsets of $${\mathbb {R}}^n$$ Rn ( $$n\ge 2$$ n≥2 ) with given measure. Our approach is based on the extension of a two-dimensional existence result of Ashbaugh and Bucur and on the idea of Alt and Caffarelli to focus on the eigenfunction.