z]]f] = 0 which represents the bi-polyanalytic functions, is investigated in the upper half plane and different forms of boundary conditions leading to the well-known Schwarz, Dirichlet and Neumann problems in complex analysis are solved in the upper half plane in .
The Neumann problems for higher-order linear complex partial differential equations are not considered in half plane, quarter plane and concentric rings.
The Neumann problem is uniquely solvable in the weak sense if and only if for any z [not member of] [[bar.
Also, in the upper half plane the Neumann problem is considered for the inhomogeneous Cauchy-Riemann equation and Poisson equation, .
The Neumann problem for analytic functions, more generally for the inhomogeneous Cauchy-Riemann equation and Poisson equation are investigated in a circular ring domain; the representations to the solutions and solvability conditions are given in an explicit form by Vaitekhovich [54-56].
for a suitable complex valued function f given in D, are the operators related to Neumann problem for generalized n-Poisson equations.
The 16 papers develop a method for calculating the upper bound of orthogonal projections in a Hilbert space, a Mosco stability theorem for the generalized proximal mapping, and three nontrivial solutions for p-Laplacian Neumann problems
The consequence of the singular local Neumann problems that arise was addressed in .
We note that these Neumann problems are always well-posed, even without any constraints on the normal component of the velocity since we have removed the constant pressure component constraints.
In addition, the FBA requires two Dirichlet local problems and one singular local Neumann problem in each iteration, whereas the BDDC requires one local Dirichlet problem and two nonsingular local Neumann problem.
Fourier series, integrals, and transforms are followed by their rigorous application to wave and diffusion equations as well as to Dirichlet and Neumann problems
He covers first-order equations, linear second-order equations, elements of Fourier analysis, the wave equation, the heat equation, Dirichlet and Neumann problems
, existence theorems, and a selection of the aforesaid advanced topics.