Dirichlet problem
Existence

The Dirichlet problem for harmonic functions always has a solution, and that solution is unique, when the boundary is sufficiently smooth and f (s) {\displaystyle f(s)} is continuous. More precisely, it has a solution when

for some α ∈ (0, 1) {\displaystyle \alpha \in (0,1)}, where C 1, α {\displaystyle C^{1,\alpha }} denotes the Hölder condition.
keywords:forbidden_words