On a transform method for the Laplace equation in a polygon

By A. S. Fokas, A. Kapaev. 2003

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Two–dimensional linear partial differential equations in a convex polygon (2001, methodology): “Several other boundary-value problems for (1.1) are discussed by Fokas & Kapaev (1999) and ben-Avraham & Fokas (1999).”
Explicit integral solutions for the plane elastostatic semi-strip (2004, methodology): “Examples of the partial differential equations considered include evolution equations as well as elliptic-type equations such as the Laplace (Fokas & Kapaev 2003) and modified Helmholtz equations (Antipov & Fokas 2004; ben-Avraham & Fokas 2001).”
An analytical method for linear elliptic PDEs and its numerical implementation (2004, background): “This is a consequence of the fact that (11) is valid for all complex values k. The analytical investigation of the global condition is discussed in [2] in general, and in [ 3 ] for the Laplace equation in particular.”
The unified method: I. Nonlinearizable problems on the half-line (2011, methodology): “In this paper, we revisit the implementation of the unified method to integrable evolution PDEs on the half-line.”