Numerical solutions of the Dirichlet problem via a density theorem
Robert J. Whitley, Theodore V. Hromadka · Numerical Methods for Partial Differential Equations · 1994
Abstract Under mild conditions a certain subspace M, consisting of functions which are analytic in a simply connected domain Ω and continuous on the boundary Gamma;, is shown to have real parts which are dense, in the sup norm, in the set of all solutions to the Dirichlet problem for continuous boundary data. Similar results hold for Lp boundary data. Numerical solutions of sample Dirichlet problems are computed. © 1994 John Wiley & Sons, Inc.