Necas' book Direct Methods in the Theory of Elliptic Equations, published 1967 in French, has become a standard reference for the mathematical theory of linear elliptic equations and systems. This English edition, translated by G. Tronel and A. Kufner, presents Necas' work essentially in the form it was published in 1967. It gives a timeless and in some sense definitive treatment of a number issues in variational methods for elliptic systems and higher order equations. The text is recommended to graduate students of partial differential equations, postdoctoral associates in Analysis, and scientists working with linear elliptic systems. In fact, any researcher using the theory of elliptic systems will benefit from having the book in his library.
The volume gives a self-contained presentation of the elliptic theory based on the "direct method", also known as the variational method. Due to its universality and close connections to numerical approximations, the variational method has become one of the most important approaches to the elliptic theory. The method does not rely on the maximum principle or other special properties of the scalar second order elliptic equations, and it is ideally suited for handling systems of equations of arbitrary order. The prototypical examples of equations covered by the theory are, in addition to the standard Laplace equation, Lame's system of linear elasticity and the biharmonic equation (both with variable coefficients, of course). General ellipticity conditions are discussed and most of the natural boundary condition is covered. The necessary foundations of the function space theory are explained along the way, in an arguably optimal manner. The standard boundary regularity requirement on the domains is the Lipschitz continuity of the boundary, which "when going beyond the scalar equations of second order" turns out to be a very natural class. These choices reflect the author's opinion that the Lame system and the biharmonic equations are just as important as the Laplace equation, and that the class of the domains with the Lipschitz continuous boundary (as opposed to smooth domains) is the most natural class of domains to consider in connection with these equations and their applications.
- ISBN:
- 9783642270734
- 9783642270734
-
Category:
- Differential calculus & equations
- Format:
- Paperback
- Publication Date:
-
29-11-2013
- Language:
- English
- Publisher:
- Springer-Verlag Berlin and Heidelberg GmbH & Co. KG
- Country of origin:
- Germany
- Pages:
- 372
- Dimensions (mm):
- 235x155x20mm
- Weight:
- 0.59kg
This title is in stock with our Australian supplier and should arrive at our Sydney warehouse within 2 - 3 weeks of you placing an order.
Once received into our warehouse we will despatch it to you with a Shipping Notification which includes online tracking.
Please check the estimated delivery times below for your region, for after your order is despatched from our warehouse:
ACT Metro: 2 working days
NSW Metro: 2 working days
NSW Rural: 2-3 working days
NSW Remote: 2-5 working days
NT Metro: 3-6 working days
NT Remote: 4-10 working days
QLD Metro: 2-4 working days
QLD Rural: 2-5 working days
QLD Remote: 2-7 working days
SA Metro: 2-5 working days
SA Rural: 3-6 working days
SA Remote: 3-7 working days
TAS Metro: 3-6 working days
TAS Rural: 3-6 working days
VIC Metro: 2-3 working days
VIC Rural: 2-4 working days
VIC Remote: 2-5 working days
WA Metro: 3-6 working days
WA Rural: 4-8 working days
WA Remote: 4-12 working days
Share This Book: