Author | Dautray, Robert. author |
---|---|
Title | Mathematical Analysis and Numerical Methods for Science and Technology [electronic resource] : Volume 4 Integral Equations and Numerical Methods / by Robert Dautray, Jacques-Louis Lions |
Imprint | Berlin, Heidelberg : Springer Berlin Heidelberg, 2000 |
Connect to | http://dx.doi.org/10.1007/978-3-642-61531-3 |
Descript | X, 493 p. online resource |
X. Mixed Problems and the Tricomi Equation -- ยง 1. Description and Formulation of the Problem -- ยง 2. Methods for Solving Problems of Mixed Type -- Bibliographic Commentary -- XI. Integral Equations -- ยง 1. The Wiener-Hopf Method -- ยง 2. Sectionally Analytic Functions -- ยง 3. The Hilbert Problem -- ยง 4. Application to Some Problems in Physics -- ยง 1. Study of Certain Weighted Sobolev Spaces -- ยง 2. Integral Equations Associated with the Boundary Value Problems of Electrostatics -- ยง 3. Integral Equations Associated with the Helmholtz Equation -- ยง 4. Integral Equations Associated with Problems of Linear Elasticity -- ยง 5. Integral Equations Associated with the Stokes System -- XII. Numerical Methods for Stationary Problems -- ยง 1. Principal Aspects of the Finite Element Method Applied to the Problem of Linear Elasticity -- ยง 2. Treatment of Domains with Curved Boundaries -- ยง 3. A Non Conforming Method of Finite Elements -- ยง 4. Applications to the Problems of Plates and Shells -- ยง 5 Approximation of Eigenvalues and Eigenvectors -- ยง 6. An Example of the Approximate Calculation for a Problem of the Eigenvalues of a Non Self-Adjoint Operator -- Review of Chapter XII -- XIII. Approximation of Integral Equations by Finite Elements. Error Analysis -- ยง 1. The Case of a Polyhedral Surface -- ยง 2. The Case of a Regular Closed Surface -- Appendix. โSingular Integralsโ -- ยง 1. Operator, Convolution Operator, Integral Operator -- ยง 2. The Hilbert Transformation -- ยง 3. Generalities on Singular Integral Operators -- ยง 5. The Calderon-Zygmund Theorem -- ยง 6. Marcinkiewicz Spaces -- 1. Definitions -- 2. Application to the Homogeneous Convolution Kernel -- 4. Operators of Weak Type. The Marcinkiewicz Theorem -- 5. The Maximal Hardy-Littlewood Operator. -- Proof of Lemma 1 in ยง 2 -- Table of Notations -- of Volumes1โ3, 5, 6