Extremal norms of the potentials recovered from inverse Dirichlet problems. (19th February 2016)

• Record Type: Journal Article
• Authors: Qi, Jiangang; Chen, Shaozhu
• Is Part Of: Inverse problems. Volume 32:Number 3(2016:Mar.)
• Publication Date: 2016-02-19
• Subjects: Sturm–Liouville problem -- inverse problem -- Lyapunov-type inequality -- bound on eigenvalue; 34B20 -- 34L99 -- 34L05; Inverse problems (Differential equations) -- Periodicals; 515.357
• DOI: 10.1088/0266-5611/32/3/035007
• Languages: English
• ISSNs: 0266-5611

Abstract

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.