Chapter 4: Elliptic Problems: Linear
A. C. L. Ashton · Society for Industrial and Applied Mathematics eBooks · 2014
4.1 ▪ Elliptic Boundary Value Problems via the Fokas Method 4.1.1 ▪ Introduction The unified method for boundary value problems was introduced by A. S. Fokas in the late nineties [7, 6] and has since been applied to a variety of problems. It can be interpreted as the Fourier analogue of the classical boundary integral techniques. The analysis takes place in the “spectral space” rather than on the physical space on which the boundary value problem is posed. The unified approach also gives a concrete realization of the fundamental principle of Ehrenpreis [5], which states that solutions to constant coefficient PDEs on convex domains can be written as a superposition of exponential solutions.