Extremal norms of the potentials recovered from inverse Dirichlet problems. (19th February 2016) - Qi, Jiangang; Chen, Shaozhu
Abstract: Consider the Sturm–Liouville eigenvalue problem, where, and its spectrum is denoted by . For a real number λ, define and . We will set up a formula for explicitly in terms of λ and specify where the infimum can be attained. As an application, we will give the extremal values of the n th eigenvalue of the Dirichlet problem for potentials on a sphere, . The proofs are based on a new Lyapunov-type inequality for Sturm–Liouville equations with potentials.