Dirichlet problem
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In mathematics, Dirichlet problems are a class of partial differential equation (PDE) problems which ask you to solve for the values of a function in a region given the value of the function on the boundary of that region. This requirement is called the Dirichlet boundary condition, for the partial differential equation that the function satisfies within the region.
Dirichlet problems are typical of elliptic partial differential equations, and potential theory, and the Laplace equation in particular. Other examples include equations involving the bilaplacian, in elasticity theory.
They are one of several types of classes of PDE problems defined by the information given at the boundary, including Neumann problems and Cauchy problems.