Isoperimetric Inequalities in a Class of Nonlinear Eigenvalue Problems
Philip S. Crooke, Ren� P. Sperb · SIAM Journal on Mathematical Analysis · 1978
In this work we prove an isoperimetric inequality for the eigenvalue $\lambda $ and other quantities in the problem $\Delta u + \lambda u^{2p + 1} = 0$ in D, $u = 0$ on $\partial D$ where D is a plane, bounded domain.