Harmonic extension
= Harmonic extension
{title2=$\Delta u=0\text{ in }\Omega,\quad u|_{\partial\Omega}=f$}
A harmonic extension of boundary data $f$ is a <harmonic function> satisfying those <Dirichlet boundary data> in a specified solution class. Existence and uniqueness depend on the domain, the regularity of the data and, on unbounded domains, growth conditions. A <Poisson kernel> constructs such an extension on standard domains.