Firstly, we prove a pointwise comparison result for the suitable symmetrized problem that depends on a small positive parameter A. Then, by these results and by the Schwarz symmetrization, we obtain some asymptotic relationship between the solutions Ue of a general e problem and a sequence of real numbers Ae. Finally, it is shown an application the preceding results to getting a priori estimate...

The performance of multigrid methods for the standard Poisson problem and for the consistent Poisson problem arising in spectral element discretizations of the Navier-Stokes equations is investigated. It is demonstrated that overlapping additive Schwarz methods are effective smoothers, provided that the solution in the overlap region is weighted by the inverse counting matrix. It is also shown ...

We develop a representation of the second kind for certain Hardy classes solutions to nonhomogeneous Cauchy–Riemann equations and use it show that boundary values in sense distributions these functions can be represented as sum an atomic decomposition error term. continuity Hilbert transform on this class Schwarz-type value problem constructed associated classes.

Abstract There are three basic boundary value problems for the inhomogeneous polyanalytic equation in planar domains, well-posed iterated Schwarz problem, and further two over-determined of Dirichlet Neumann type. These investigated domains having a harmonic Green function. For treated earlier [Ü. Aksoy, H. Begehr, A.O. Çelebi, AV Bitsadze’s observation on bianalytic functions problem. Complex ...