Some Explicit Solutions of the Shape Equation
Abstract
The consideration of the variational problem for minimization of the bending energy of membrane surfaces under some natural geometric constraints leads to the so called general shape equation. The available analytical solutions of this equation including a new one are reviewed in some detail.
 Publication:

Application of Mathematics in Technical and Natural Sciences
 Pub Date:
 November 2010
 DOI:
 10.1063/1.3526617
 Bibcode:
 2010AIPC.1301..215M
 Keywords:

 integral equations;
 mathematical operators;
 partial differential equations;
 functional analysis;
 02.30.Rz;
 02.30.Vv;
 02.30.Jr;
 02.30.Sa;
 Integral equations;
 Operational calculus;
 Partial differential equations;
 Functional analysis