Dirichlet problem

Suppose $\\Omega$ is a domain of $\\mathbb{R}^{n}$ and $\\partial\\Omega$ is the boundary of $\\Omega$ .Further suppose $f$ is a function $f\\colon\\partial\\Omega\\to\\mathbb{C}$ . Then theDirichlet problem is to find a function $\\phi\\colon\\Omega\\cup\\partial\\Omega\\to\\mathbb{C}$ such that

	$\\displaystyle\\phi$	$\\displaystyle=$	$\\displaystyle f,\\quad\\text{on $\\partial\\Omega$},$
	$\\displaystyle\abla^{2}\\phi$	$\\displaystyle=$	$\\displaystyle 0,\\quad\\text{in $\\Omega$}.$