Local inverse estimates for non-local boundary integral operators

Local inverse estimates for non-local boundary integral operators

We prove local inverse-type estimates for the four non-local boundary integral operators associated with the Laplace operator on a bounded Lipschitz domain Ω in R for d ≥ 2 with piecewise smooth boundary. For piecewise polynomial ansatz spaces and d ∈ {2, 3}, the inverse estimates are explicit in both the local mesh width and the approximation order. An application to efficiency estimates in a ...

Novel Inverse Estimates for Non-Local Operators

Nvestigation of a Boundary Layer Problem for Perturbed Cauchy-Riemann Equation with Non-local Boundary Condition

Boundary layer problems (Singular perturbation problems) more have been applied for ordinary differential equations. While this theory for partial differential equations have many applications in several fields of physics and engineering. Because of complexity of limit and boundary behavior of the solutions of partial differential equations these problems considered less than ordinary case. In ...

Analytic solutions for the Stephen's inverse problem with local boundary conditions including Elliptic and hyperbolic equations

In this paper, two inverse problems of Stephen kind with local (Dirichlet) boundary conditions are investigated. In the first problem only a part of boundary is unknown and in the second problem, the whole of boundary is unknown. For the both of problems, at first, analytic expressions for unknown boundary are presented, then by using these analytic expressions for unknown boundaries and bounda...

Local Approximation Estimates for a Certain Family of Summation-Integral Type Operators

In 1988, Felten obtained local and global approximation theorems for positive linear operators. In the last decade, Finta studied direct local and global approximation theorems for Baskakov type operators and SzaszMirakian type operators. In the present paper, we establish some local approximation estimates for a new family of beta operators, by using Ditzian-Totik modulus of smoothness.