Journal article
The inradius, the first eigenvalue, and the torsional rigidity of curvilinear polygons
Bulletin of the London Mathematical Society, Vol.42, pp.765-783
Oct/2010
Abstract
Let lambda(1), P, and. denote the first eigenvalue of the Dirichlet Laplacian, the torsional rigidity, and the inradius of a planar domain Omega, respectively. In this paper, we prove several inequalities for.1, P, and. in the case when Omega is a curvilinear polygon with n sides, each of which is a smooth arc of curvature at most.. Our main proofs rely on the method of dissymmetrization and on a special geometrical ` containment theorem' for curvilinear polygons. For rectilinear n- gons, which constitute a proper subclass of curvilinear n- gons with curvature at most 0, these inequalities were established by the first author in 1992. In the simplest particular case of Euclidean triangles T, the inequality linking the first eigenvalue and the inradius of T is equivalent to the inequality.1
Details
- Title
- The inradius, the first eigenvalue, and the torsional rigidity of curvilinear polygons
- Creators
- Alexander Yu. Solynin (null)Victor A. Zalgaller (null)
- Resource Type
- Journal article
- Publication Details
- Bulletin of the London Mathematical Society, Vol.42, pp.765-783; Oct/2010
- Number of pages
- 19
- Language
- English
- DOI
- https://doi.org/10.1112/blms/bdq028
- Scientific Unit
- The Weizmann Institute of Science
- Record Identifier
- 993266764203596
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