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Introduction to regularity theory for nonlinear elliptic systems

Author: Mariano Giaquinta
Publisher: Basel ; Boston : Birkhäuser, 1993.
Series: Lectures in mathematics ETH Zürich.
Edition/Format:   Print book : EnglishView all editions and formats
Summary:

These lectures are an introduction to the regularity theory of minimizers of variational integrals, in the calculus of variations and of solutions of nonlinear elliptic systems. Topics covered  Read more...

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Additional Physical Format: Online version:
Giaquinta, Mariano, 1947-
Introduction to regularity theory for nonlinear elliptic systems.
Basel ; Boston : Birkhäuser, 1993
(OCoLC)624454456
Material Type: Internet resource
Document Type: Book, Internet Resource
All Authors / Contributors: Mariano Giaquinta
ISBN: 3764328797 9783764328795 0817628797 9780817628796
OCLC Number: 28339598
Description: viii, 130 pages : illustrations ; 24 cm.
Contents: 1. Direct methods in the calculus of variations: existence --
1.1. Hilbert-space approach: Existence theorems --
1.2. Direct methods in the calculus of variations: semicontinuity-theorems --
2. Difference-quotient-method and linearisation of nonlinear systems; Hilbert-space regularity --
2.1. Introduction --
2.2. The Caccioppoli-inequality --
2.3. The difference-quotient-method --
2.4. Hilbert-space regularity: interior regularity --
2.5. Hilbert-space regularity: boundary regularity --
2.6. Linearization of nonlinear equations --
3. Schauder-estimates --
3.1. Morrey- and Campanato-spaces --
3.2. (Interior- ) Schauder-estimates for elliptic systems in divergence form --
3.3. (Interior)-Schauder estimates for elliptic systems in non-divergence form --
3.4. Regularity up to the boundary: Dirichlet-boundary-value problem --
3.5. A few simple applications to nonlinear equations --
4. L[superscript p]-theory --
4.1. Some preliminaries --
4.2. The spaces of functions of bounded mean-oscillation = BMO-spaces = John-Nirenberg-spaces --
4.3. L[superscript p]-theory --
5. Regularity in the scalar case --
5.1. De Giorgi's class and De Giorgi's theorem --
5.2. Moser's iteration technique --
5.3. De Giorgi-class and Harnack-inequality --
5.4. Quasi-minima --
5.5. Holder-continuity of derivatives of minimizers --
6. Regularity in the vector-valued case --
6.1. A simple case --
6.2. Reverse Holder-inequality with increasing support --
6.3. Some model results --
6.4. The singular set of minimizers of a special class of quadratic functionals.
Series Title: Lectures in mathematics ETH Zürich.
Responsibility: Mariano Giaquinta.
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"Giaquinta...and Modica...present the differential and integral calculus for real functions of a single real variable from a sophisticated point of view. Their book is far better suited as a source Read more...

 
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