In this sense, we study the following Dirichlet problem
of a complex Monge-Ampere type
In that case, as a remedy, one should switch the interface conditions and solve a Dirichlet problem
on the larger subdomain.
It is known that the Poisson kernel function is an analogue of the Cauchy kernel for the analytic functions and the Poisson integral formula solves the Dirichlet problem
for the inhomogeneous Laplace equation.
The method of least squares on the boundary was also used in  to solve the first Dirichlet problem
We consider the following auxiliary Dirichlet problem
Zhang; Nonexistence of positive classical solutions of a singular nonlinear Dirichlet problem
with a convection term, Nonlinear Analysis 8 (1996) 957-961
Grebennikov, Fast algorithm for solution of Dirichlet problem
for Laplace equation, WSEAS Transactions on Computers Journal, 2(4), pp.
Normalization of the Solutions to Dirichlet Problem
RICCERI, On the Dirichlet problem
involving nonlinearities with non-positive primitive: a problem and a remark, Appl.
GE, Infinitely many positive solutions of a singular Dirichlet problem
involving the p-Laplacian, Commun.
From the uniqueness theorem for the exterior Dirichlet problem
[5,6] we obtain div [u.
No date is cited for the first edition, but to this second has been added a final chapter on the existence of solutions, primarily the Dirichlet problem
for various types of elliptic equations.