A direct proof of the equivalence between Dirichlet's principle and Perron's method

Tsogtgerel Gantumur

We give a short proof that for a bounded domain $\Omega \subset {\mathbb{R}}^n$ and continuous boundary data $g\in C(\partial \Omega )$ admitting a continuous finite-energy extension $ϕ\in H^{1}(Ω…