Editing Dirichlet problem (section)

===Existence===
The Dirichlet problem for harmonic functions always has a solution, and that solution is unique, when the boundary is sufficiently smooth and <math>f(s)</math> is continuous. More precisely, it has a solution when

: <math>\partial D \in C^{1,\alpha}</math>

for some <math>\alpha \in (0, 1)</math>, where <math>C^{1,\alpha}</math> denotes the [[Hölder condition]].