On Some Boundary Value Problems for the Equation nabla \cdot (F(nabla w)nabla 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} = partial w/partial x, γ _{y} = partial w/partial y is used to deduce solutions of the equation nabla \cdot (F(nabla w)nabla w) = 0 for various boundary value problems. The method is applied, in principle, to general (F(nabla w) and specific examples, previously treated by other methods (e.g. F(nabla w) = nabla w^{N}), are worked out in detail as a check on the method.
 Publication:

Proceedings of the Royal Society of London Series A
 Pub Date:
 February 1995
 DOI:
 10.1098/rspa.1995.0016
 Bibcode:
 1995RSPSA.448..269A