Symmetry for Elliptic PDEs

Symmetry for Elliptic PDEs

Author: Alberto Farina

Publisher: American Mathematical Soc.

Published: 2010

Total Pages: 152

ISBN-13: 0821848046

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Contains contributions from the INdAM School on Symmetry for Elliptic PDEs, which marked ""30 years after a conjecture of De Giorgi, and related problems"" and provided an opportunity for experts to discuss the state of the art and open questions on the subject.


Proceedings Of The International Congress Of Mathematicians 2018 (Icm 2018) (In 4 Volumes)

Proceedings Of The International Congress Of Mathematicians 2018 (Icm 2018) (In 4 Volumes)

Author: Boyan Sirakov

Publisher: World Scientific

Published: 2019-02-27

Total Pages: 5393

ISBN-13: 9813272899

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The Proceedings of the ICM publishes the talks, by invited speakers, at the conference organized by the International Mathematical Union every 4 years. It covers several areas of Mathematics and it includes the Fields Medal and Nevanlinna, Gauss and Leelavati Prizes and the Chern Medal laudatios.


Elliptic Partial Differential Equations and Quasiconformal Mappings in the Plane

Elliptic Partial Differential Equations and Quasiconformal Mappings in the Plane

Author: Kari Astala

Publisher: Princeton University Press

Published: 2008-12-29

Total Pages: 696

ISBN-13: 1400830117

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This book explores the most recent developments in the theory of planar quasiconformal mappings with a particular focus on the interactions with partial differential equations and nonlinear analysis. It gives a thorough and modern approach to the classical theory and presents important and compelling applications across a spectrum of mathematics: dynamical systems, singular integral operators, inverse problems, the geometry of mappings, and the calculus of variations. It also gives an account of recent advances in harmonic analysis and their applications in the geometric theory of mappings. The book explains that the existence, regularity, and singular set structures for second-order divergence-type equations--the most important class of PDEs in applications--are determined by the mathematics underpinning the geometry, structure, and dimension of fractal sets; moduli spaces of Riemann surfaces; and conformal dynamical systems. These topics are inextricably linked by the theory of quasiconformal mappings. Further, the interplay between them allows the authors to extend classical results to more general settings for wider applicability, providing new and often optimal answers to questions of existence, regularity, and geometric properties of solutions to nonlinear systems in both elliptic and degenerate elliptic settings.


Partial Differential Equations of Elliptic Type

Partial Differential Equations of Elliptic Type

Author: C. Miranda

Publisher: Springer Science & Business Media

Published: 2012-12-06

Total Pages: 384

ISBN-13: 3642877737

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In the theory of partial differential equations, the study of elliptic equations occupies a preeminent position, both because of the importance which it assumes for various questions in mathematical physics, and because of the completeness of the results obtained up to the present time. In spite of this, even in the more classical treatises on analysis the theory of elliptic equations has been considered and illustrated only from particular points of view, while the only expositions of the whole theory, the extremely valuable ones by LICHTENSTEIN and AscoLI, have the charac ter of encyclopedia articles and date back to many years ago. Consequently it seemed to me that it would be of some interest to try to give an up-to-date picture of the present state of research in this area in a monograph which, without attaining the dimensions of a treatise, would nevertheless be sufficiently extensive to allow the expo sition, in some cases in summary form, of the various techniques used in the study of these equations.


Symmetry Methods for Differential Equations

Symmetry Methods for Differential Equations

Author: Peter Ellsworth Hydon

Publisher: Cambridge University Press

Published: 2000-01-28

Total Pages: 230

ISBN-13: 9780521497862

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This book is a straightforward introduction to the subject of symmetry methods for solving differential equations, and is aimed at applied mathematicians, physicists, and engineers. The presentation is informal, using many worked examples to illustrate the main symmetry methods. It is written at a level suitable for postgraduates and advanced undergraduates, and is designed to enable the reader to master the main techniques quickly and easily.The book contains some methods that have not previously appeared in a text. These include methods for obtaining discrete symmetries and integrating factors.


Recent Trends in Operator Theory and Partial Differential Equations

Recent Trends in Operator Theory and Partial Differential Equations

Author: Vladimir Maz'ya

Publisher: Birkhäuser

Published: 2017-02-23

Total Pages: 313

ISBN-13: 3319470795

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This volume is dedicated to the eminent Georgian mathematician Roland Duduchava on the occasion of his 70th birthday. It presents recent results on Toeplitz, Wiener-Hopf, and pseudodifferential operators, boundary value problems, operator theory, approximation theory, and reflects the broad spectrum of Roland Duduchava's research. The book is addressed to a wide audience of pure and applied mathematicians.


Elliptic Partial Differential Equations

Elliptic Partial Differential Equations

Author: Qing Han

Publisher: American Mathematical Soc.

Published: 2011

Total Pages: 161

ISBN-13: 0821853139

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This volume is based on PDE courses given by the authors at the Courant Institute and at the University of Notre Dame, Indiana. Presented are basic methods for obtaining various a priori estimates for second-order equations of elliptic type with particular emphasis on maximal principles, Harnack inequalities, and their applications. The equations considered in the book are linear; however, the presented methods also apply to nonlinear problems.


Handbook of Differential Equations:Stationary Partial Differential Equations

Handbook of Differential Equations:Stationary Partial Differential Equations

Author: Michel Chipot

Publisher: Elsevier

Published: 2005-08-19

Total Pages: 625

ISBN-13: 0080461077

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A collection of self contained, state-of-the-art surveys. The authors have made an effort to achieve readability for mathematicians and scientists from other fields, for this series of handbooks to be a new reference for research, learning and teaching.Partial differential equations represent one of the most rapidly developing topics in mathematics. This is due to their numerous applications in science and engineering on the one hand and to the challenge and beauty of associated mathematical problems on the other.Key features:- Self-contained volume in series covering one of the most rapid developing topics in mathematics.- 7 Chapters, enriched with numerous figures originating from numerical simulations.- Written by well known experts in the field.- Self-contained volume in series covering one of the most rapid developing topics in mathematics.- 7 Chapters, enriched with numerous figures originating from numerical simulations.- Written by well known experts in the field.


Elliptic Differential Operators and Spectral Analysis

Elliptic Differential Operators and Spectral Analysis

Author: D. E. Edmunds

Publisher: Springer

Published: 2018-11-20

Total Pages: 324

ISBN-13: 3030021254

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This book deals with elliptic differential equations, providing the analytic background necessary for the treatment of associated spectral questions, and covering important topics previously scattered throughout the literature. Starting with the basics of elliptic operators and their naturally associated function spaces, the authors then proceed to cover various related topics of current and continuing importance. Particular attention is given to the characterisation of self-adjoint extensions of symmetric operators acting in a Hilbert space and, for elliptic operators, the realisation of such extensions in terms of boundary conditions. A good deal of material not previously available in book form, such as the treatment of the Schauder estimates, is included. Requiring only basic knowledge of measure theory and functional analysis, the book is accessible to graduate students and will be of interest to all researchers in partial differential equations. The reader will value its self-contained, thorough and unified presentation of the modern theory of elliptic operators.