The Dirichlet problem for the diffusion equation in the exterior of non-closed Lipschitz surfaces
П. А. Крутицкий · AIP conference proceedings · 2012
We study the Dirichlet problem for the stationary diffusion equation in the exterior of non-closed Lipschitz surfaces in R3. The Dirichlet problem for a Laplace equation is a particular case of our problem. Theorems on existence and uniqueness of a weak solution of the problem are proved. The integral representation for a solution is obtained in the form of single layer potential. The density in the potential is defined as a solution of the operator (integral) equation, which is uniquely solvable.