On some boundary value problems for the equation ∇ • ( F (|∇ w |)∇ w ) = 0

Abstract

A method based on the use of a reciprocal theorem and dual functions in the strain plane ( γ x , γ y ), where γ x = ∂ w /∂ x , γ y = ∂ w /∂ y is used to deduce solutions of the equation ∇ • ( F (│∇ w │∇ w ) = 0 for various boundary value problems. The method is applied, in principle, to general (F(│∇ w │) and specific examples, previously treated by other methods (e. g. F (│∇ w │) = │∇ w │ N ), are worked out in detail as a check on the method.