Counterexample to Dirichlet principle

Let Ω be an open set in some Euclidean space and v a real-valued function on Ω. Dirichlet principle Dirichlet’s integral for v, also called the Dirichlet energy of v, is Among functions with specified values on the boundary of Ω, Dirichlet’s principle says that minimizing Dirichlet’s integral is equivalent to solving Laplace’s equation. In […]...

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