An isoperimetric type inequality for the principal eigenvalue of Schrodinger operators depending on the curvature of a loop

作者：Stefanopoulos Vangelis^*

来源：Journal of Differential Equations, 2016, 260(1): 115-132.

DOI：10.1016/j.jde.2015.08.046

• Isoperimetric inequality
• Curvature of a loop
• Schrodinger operator
• Principal eigenvalue
• Riccati equation

Let K be the curvature of a smooth closed curve of length 2 pi. The 2 pi-periodic eigenvalue problems u '' g kappa(2) u + lambda u = 0, where g is a real parameter, are considered and upper and lower bounds for their principal eigenvalues are obtained. The bounds are of isoperimetric type and characterize uniquely the curve in the case where equality occurs.

• 出版日期2016-1-5