Bounds for the Change in the Solutions of Second Order Elliptic Partial Differential Equation's When the Boundary is Perturbed
Bounds for the Change in the Solutions of Second Order Elliptic Partial Differential Equation's When the Boundary is Perturbed

Author: J. J. Blair

Publisher:

Published: 1971

Total Pages: 21

ISBN-13:

DOWNLOAD EBOOK

Let omega be a smooth bounded subset of (R sup N) and L be a uniformly elliptic second order differential operator with smooth coefficients. The author obtains a bound for the difference between the solution, u, to the equation Lu = f in omega with the Dirichlet boundary conditions: u = 0 on boundary omega, and the solution, u prime, to corresponding boundary value problem on a non-smooth domain omega prime which appriximates omega. The magnitude of the bound depends only on the Euclidean distance between the domains omega and omega prime. (Author).

Bounds for Solutions of Second Order Elliptic Partial Differential Equations
Bounds for Solutions of Second Order Elliptic Partial Differential Equations

Author: James H. Bramble

Publisher:

Published: 1961

Total Pages: 64

ISBN-13:

DOWNLOAD EBOOK

In this paper pointwise a priori bounds are obtained for the solution of the Dirichlet problem associated with a rather general second order elliptic differential operator. These bounds involve only integrals of the data itself and not of its derivatives. Furthermore, the bounds obtained are applicable at any point in the domain of definition (i.e. up to the boundary of the region).

Boundary Value Problems For Second Order Elliptic Equations
Boundary Value Problems For Second Order Elliptic Equations

Author: A.V. Bitsadze

Publisher: Elsevier

Published: 2012-12-02

Total Pages: 212

ISBN-13: 0323162266

DOWNLOAD EBOOK

Applied Mathematics and Mechanics, Volume 5: Boundary Value Problems: For Second Order Elliptic Equations is a revised and augmented version of a lecture course on non-Fredholm elliptic boundary value problems, delivered at the Novosibirsk State University in the academic year 1964-1965. This seven-chapter text is devoted to a study of the basic linear boundary value problems for linear second order partial differential equations, which satisfy the condition of uniform ellipticity. The opening chapter deals with the fundamental aspects of the linear equations theory in normed linear spaces. This topic is followed by discussions on solutions of elliptic equations and the formulation of Dirichlet problem for a second order elliptic equation. A chapter focuses on the solution equation for the directional derivative problem. Another chapter surveys the formulation of the Poincaré problem for second order elliptic systems in two independent variables. This chapter also examines the theory of one-dimensional singular integral equations that allow the investigation of highly important classes of boundary value problems. The final chapter looks into other classes of multidimensional singular integral equations and related boundary value problems.

Perturbation of the Boundary in Boundary-Value Problems of Partial Differential Equations
Perturbation of the Boundary in Boundary-Value Problems of Partial Differential Equations

Author: Dan Henry

Publisher: Cambridge University Press

Published: 2005-05-26

Total Pages: 220

ISBN-13: 9781139441179

DOWNLOAD EBOOK

Perturbation of the boundary is a rather neglected topic in the study of partial differential equations, in part because it often entails long and difficult caluclations. In this book, first published in 2005, the author carefully discusses a calculus that overcomes the computational morass, and he goes on to develop more general forms of standard theorems, helping to answer a problems involving boundary perturbations.

Pointwise Bounds for Solutions of the Cauchy Problem for Elliptic Equations
Pointwise Bounds for Solutions of the Cauchy Problem for Elliptic Equations

Author: George Norman Trytten

Publisher:

Published: 1962

Total Pages: 92

ISBN-13:

DOWNLOAD EBOOK

An analysis is presented which deals with a technique for approximating the solution to a Cauchy problem for a geneal second-order elliptic patil differential equation defined in an N-dimensional region D. The method is based upon the determination of an a priori bound for the value of an arbitrary function u at a point P in D in terms of the values of u and its gradient on the cauchy surface andA FUNCTIONAL OF THE ELLIPTIC OPERATOR APPLIED TO U. (Author).