Calculus of Variations and Geometric Measure Theory
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G. Crasta - I. Fragalà - F. Gazzola

On a long-standing conjecture by Pólya-Szegö and related topics

created on 10 Dec 2003
modified by fragala on 18 Jan 2006


Published Paper

Inserted: 10 dec 2003
Last Updated: 18 jan 2006

Journal: Zeit. Angew. Math. Phys.
Volume: 56
Number: 5
Pages: 763-782
Year: 2005


The electrostatic capacity of a convex body is usually not simple to compute. We discuss two possible approximations of it. The first one is related to a long-standing conjecture by Pólya-Szegö. It states that, among all convex bodies, the ``worst shape'' for the approximation exists and is the planar disk. We prove the first part of this conjecture, and we establish some related results which give further evidence for the validity of the second part. We also suggest some complementary conjectures and open problems. The second approximation we study is based on the use of web functions.

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