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Author: Alain Bensoussan
Publisher: Springer Science & Business Media
ISBN: 3662129051
Category : Mathematics
Languages : en
Pages : 450
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Book Description
This book collects many helpful techniques for obtaining regularity results for solutions of nonlinear systems of partial differential equations. These are applied in various cases to provide useful examples and relevant results, particularly in such fields as fluid mechanics, solid mechanics, semiconductor theory and game theory.
Author: Alain Bensoussan
Publisher: Springer Science & Business Media
ISBN: 3662129051
Category : Mathematics
Languages : en
Pages : 450
Get Book Here
Book Description
This book collects many helpful techniques for obtaining regularity results for solutions of nonlinear systems of partial differential equations. These are applied in various cases to provide useful examples and relevant results, particularly in such fields as fluid mechanics, solid mechanics, semiconductor theory and game theory.
Author: Alain Bensoussan
Publisher:
ISBN: 9783662129067
Category :
Languages : en
Pages : 456
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Book Description
Author: Charles B. Morrey
Publisher:
ISBN:
Category :
Languages : en
Pages :
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Author: Sergio Campanato
Publisher:
ISBN:
Category :
Languages : en
Pages : 0
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Author: Frank Duzaar
Publisher:
ISBN:
Category :
Languages : en
Pages : 24
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Author: Mariano Giaquinta
Publisher: Springer Science & Business Media
ISBN: 8876424431
Category : Mathematics
Languages : en
Pages : 373
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Book Description
This volume deals with the regularity theory for elliptic systems. We may find the origin of such a theory in two of the problems posed by David Hilbert in his celebrated lecture delivered during the International Congress of Mathematicians in 1900 in Paris: 19th problem: Are the solutions to regular problems in the Calculus of Variations always necessarily analytic? 20th problem: does any variational problem have a solution, provided that certain assumptions regarding the given boundary conditions are satisfied, and provided that the notion of a solution is suitably extended? During the last century these two problems have generated a great deal of work, usually referred to as regularity theory, which makes this topic quite relevant in many fields and still very active for research. However, the purpose of this volume, addressed mainly to students, is much more limited. We aim to illustrate only some of the basic ideas and techniques introduced in this context, confining ourselves to important but simple situations and refraining from completeness. In fact some relevant topics are omitted. Topics include: harmonic functions, direct methods, Hilbert space methods and Sobolev spaces, energy estimates, Schauder and L^p-theory both with and without potential theory, including the Calderon-Zygmund theorem, Harnack's and De Giorgi-Moser-Nash theorems in the scalar case and partial regularity theorems in the vector valued case; energy minimizing harmonic maps and minimal graphs in codimension 1 and greater than 1. In this second deeply revised edition we also included the regularity of 2-dimensional weakly harmonic maps, the partial regularity of stationary harmonic maps, and their connections with the case p=1 of the L^p theory, including the celebrated results of Wente and of Coifman-Lions-Meyer-Semmes.
Author: Felix E. Browder
Publisher: American Mathematical Soc.
ISBN: 0821814729
Category : Mathematics
Languages : en
Pages : 591
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Book Description
Author: Lisa Beck
Publisher: Springer
ISBN: 3319274856
Category : Mathematics
Languages : en
Pages : 214
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Book Description
These lecture notes provide a self-contained introduction to regularity theory for elliptic equations and systems in divergence form. After a short review of some classical results on everywhere regularity for scalar-valued weak solutions, the presentation focuses on vector-valued weak solutions to a system of several coupled equations. In the vectorial case, weak solutions may have discontinuities and so are expected, in general, to be regular only outside of a set of measure zero. Several methods are presented concerning the proof of such partial regularity results, and optimal regularity is discussed. Finally, a short overview is given on the current state of the art concerning the size of the singular set on which discontinuities may occur. The notes are intended for graduate and postgraduate students with a solid background in functional analysis and some familiarity with partial differential equations; they will also be of interest to researchers working on related topics.
Author: Marcus Rang
Publisher:
ISBN:
Category :
Languages : en
Pages :
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Author: Sergio Campanato
Publisher:
ISBN:
Category :
Languages : it
Pages : 22
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