Error Estimates for Galerkin Methods for Quasilinear Parabolic and Elliptic Differential Equations in Divergence Form.
Error estimates for the Ultra Weak Variational Formulation of the Helmholtz equation
The Ultra Weak Variational Formulation (UWVF) of the Helmholtz equation provides a variational framework suitable for discretization using plane wave solutions of an appropriate adjoint equation. Currently convergence of the method is only proved on the boundary of the domain. However substantial computational evidence exists showing that the method also converges throughout the domain of the Helmholtz equation. In this paper we exploit the fact that the UWVF is essentially an upwind discontinuous...
Error estimation and optimization of the functional algorithms of a random walk on a grid which are applied to solving the Dirichlet problem for the Helmholtz equation.
Error-Bounds for Finite Element Method.
Estimates for Multigrid Methods Based on Red-Black Gauss-Seidel Smoothings.
Estimates for the Asymptotic Behavior of Solutions of the Helmholtz Equation, with an Application to Second order Elliptic Differential Operators with Variable Coefficients.
Estimates for the asymptotic behavior of solutions of the Helmholtz equation, with an application to second order elliptic differential operators with variable coefficients (Erratum).
Estimates for the Classical Parametrix for the Laplacian.
Estimates for the parametrix of the Kohn Laplacian on certain domains.
Estimation de l'erreur sur le coefficient de la singularité de la solution d'un problème elliptique sur un ouvert avec coin
Estimations of the best constant involving the norm in Wente’s inequality
Exact solutions to some external mixed problems in potential theory
A new and elegant procedure is proposed for the solution of mixed potential problems in a half-space with a circular line of division of boundary conditions. The approach is based on a new type of integral operators with special properties. Two general external problems are solved; i) An arbitrary potential is specified at the boundary outside a circle, and its normal derivative is zero inside; ii) An arbitrary normal derivative is given outside the circle, and be potential is zero inside. Several...
Excitation of shear waves in a piezoceramic medium with partially electrodized tunnel openings strengthened by a rigid stringer.
Existence and uniqueness of the solution of Laplace's equation from a model of magnetic recording.
Existence of quadrature surfaces for uniform density supported by a segment.
Existence of solutions to the Poisson equation in -weighted spaces
We examine the Poisson equation with boundary conditions on a cylinder in a weighted space of , p≥ 3, type. The weight is a positive power of the distance from a distinguished plane. To prove the existence of solutions we use our result on existence in a weighted L₂ space.
Existence of solutions to the Poisson equation in L₂-weighted spaces
We consider the Poisson equation with the Dirichlet and the Neumann boundary conditions in weighted Sobolev spaces. The weight is a positive power of the distance to a distinguished plane. We prove the existence of solutions in a suitably defined weighted space.
Existence results for a nonlinear problem modeling the displacement of a solid in a transverse flow
Existence results for -Laplacian boundary value problems on time scales.
Explicit Solutions of Nonlocal Boundary Value Problems, Containing Bitsadze-Samarskii Constraints
MSC 2010: 44A35, 35L20, 35J05, 35J25In this paper are found explicit solutions of four nonlocal boundary value problems for Laplace, heat and wave equations, with Bitsadze-Samarskii constraints based on non-classical one-dimensional convolutions. In fact, each explicit solution may be considered as a way for effective summation of a solution in the form of nonharmonic Fourier sine-expansion. Each explicit solution, may be used for numerical calculation of the solutions too.