Uniqueness for the Dirichlet Problem (Laplace Equation)
theoremAnalysisPDEthm:pde-dirichlet-uniqueness-laplace-2026aIf U is bounded and u,v\in C^2(U)\cap C(\overline U) satisfy \Delta u=\Delta v=0 in U and u=v on \partial U, then u\equiv v in U.
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