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Reduction of the Dirichlet problem to an initial value problem.

Although the derivation is concerned with solutions for plane regions with prescribed boundary values, the approach presented could by easily generalized to higher dimensions. The initial-value method is derived by a combination of invariant imbedding techniques and the Fredholm integral equation method of representation of the potential as a function of a dilayer distribution on the boundary of the region in question.

Kalaba, R.↗