The electrostatic capacity of a convex body is usually not simple to compute. Almost one century ago, Aichi-Russell suggested a simple approximate formula which involves the 2-dimensional measure of the boundary of the convex body. This approximation is estimated by what physicists usually call ``shape factor'', roughly speaking the ratio between the capacity and the approximate capacity. We discuss a long-standing conjecture by P\'olya-Szeg\"o. It says that the minimum of the ratio is attained by the 2-dimensional disk.
On a long-standing conjecture by Polya-Szego and related topics / Crasta, Graziano; Fragala', I.; Gazzola, F.. - In: ZEITSCHRIFT FUR ANGEWANDTE MATHEMATIK UND PHYSIK. - ISSN 0044-2275. - STAMPA. - 56:(2005), pp. 763-782. [10.1007/s00033-005-3092-9]
On a long-standing conjecture by Polya-Szego and related topics
CRASTA, Graziano;
2005
Abstract
The electrostatic capacity of a convex body is usually not simple to compute. Almost one century ago, Aichi-Russell suggested a simple approximate formula which involves the 2-dimensional measure of the boundary of the convex body. This approximation is estimated by what physicists usually call ``shape factor'', roughly speaking the ratio between the capacity and the approximate capacity. We discuss a long-standing conjecture by P\'olya-Szeg\"o. It says that the minimum of the ratio is attained by the 2-dimensional disk.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
