Krein [1] mentioned that for each PD equation we have two extreme operators, one is the minimal in which solution and its derivatives on the boundary are zero, the other one is the maximal operator in which there is no prescribed boundary conditions. They claim it is not possible to have a related boundary value problem for an arbitrarily chosen operator in between. They have only considered lo...

krein [1] mentioned that for each pd equation we have two extreme operators, one is the minimal in which solution and its derivatives on the boundary are zero, the other one is the maximal operator in which there is no prescribed boundary conditions. they claim it is not possible to have a related boundary value problem for an arbitrarily chosen operator in between. they have only considered lo...

An analytic solution is presented describing ̄ow to a drain in a semi-in®nite domain bounded by a leaky layer of constant thickness. The solution is developed by applying the method of images to two parallel boundaries: an inhomogeneity boundary and an equipotential boundary. It is then demonstrated that the solution for the problem with the leaky layer approximated by a leaky boundary (a mixed...

We construct a series of examples of planar isospectral domains with mixed Dirichlet-Neumann boundary conditions. This is a modification of a classical problem proposed by M. Kac.

A bstract We compute the Hamiltonian surface charges of gravity for a family conservative boundary conditions, that include Dirichlet, Neumann, and York’s mixed conditions defined by holding fixed conformal induced metric trace extrinsic curvature. show all considered, canonical methods give same answer as covariant phase space improved Lagrangian, prescription recently developed in literature ...