Geometric Analysis and Nonlinear Partial Differential Equations
Title | Geometric Analysis and Nonlinear Partial Differential Equations PDF eBook |
Author | Stefan Hildebrandt |
Publisher | Springer Science & Business Media |
Pages | 663 |
Release | 2012-12-06 |
Genre | Mathematics |
ISBN | 3642556272 |
This book is not a textbook, but rather a coherent collection of papers from the field of partial differential equations. Nevertheless we believe that it may very well serve as a good introduction into some topics of this classical field of analysis which, despite of its long history, is highly modem and well prospering. Richard Courant wrote in 1950: "It has always been a temptationfor mathematicians to present the crystallized product of their thought as a deductive general theory and to relegate the individual mathematical phenomenon into the role of an example. The reader who submits to the dogmatic form will be easily indoctrinated. Enlightenment, however, must come from an understanding of motives; live mathematical development springs from specific natural problems which can be easily understood, but whose solutions are difficult and demand new methods or more general significance. " We think that many, if not all, papers of this book are written in this spirit and will give the reader access to an important branch of analysis by exhibiting interest ing problems worth to be studied. Most of the collected articles have an extensive introductory part describing the history of the presented problems as well as the state of the art and offer a well chosen guide to the literature. This way the papers became lengthier than customary these days, but the level of presentation is such that an advanced graduate student should find the various articles both readable and stimulating.
Nonlinear PDEs, Their Geometry, and Applications
Title | Nonlinear PDEs, Their Geometry, and Applications PDF eBook |
Author | Radosław A. Kycia |
Publisher | Springer |
Pages | 279 |
Release | 2019-05-18 |
Genre | Mathematics |
ISBN | 3030170314 |
This volume presents lectures given at the Summer School Wisła 18: Nonlinear PDEs, Their Geometry, and Applications, which took place from August 20 - 30th, 2018 in Wisła, Poland, and was organized by the Baltic Institute of Mathematics. The lectures in the first part of this volume were delivered by experts in nonlinear differential equations and their applications to physics. Original research articles from members of the school comprise the second part of this volume. Much of the latter half of the volume complements the methods expounded in the first half by illustrating additional applications of geometric theory of differential equations. Various subjects are covered, providing readers a glimpse of current research. Other topics covered include thermodynamics, meteorology, and the Monge–Ampère equations. Researchers interested in the applications of nonlinear differential equations to physics will find this volume particularly useful. A knowledge of differential geometry is recommended for the first portion of the book, as well as a familiarity with basic concepts in physics.
Nonlinear partial differential equations in differential geometry
Title | Nonlinear partial differential equations in differential geometry PDF eBook |
Author | Robert Hardt |
Publisher | American Mathematical Soc. |
Pages | 356 |
Release | 1996 |
Genre | Mathematics |
ISBN | 9780821804315 |
This book contains lecture notes of minicourses at the Regional Geometry Institute at Park City, Utah, in July 1992. Presented here are surveys of breaking developments in a number of areas of nonlinear partial differential equations in differential geometry. The authors of the articles are not only excellent expositors, but are also leaders in this field of research. All of the articles provide in-depth treatment of the topics and require few prerequisites and less background than current research articles.
Geometry and Nonlinear Partial Differential Equations
Title | Geometry and Nonlinear Partial Differential Equations PDF eBook |
Author | Vladimir Oliker |
Publisher | American Mathematical Soc. |
Pages | 166 |
Release | 1992 |
Genre | Mathematics |
ISBN | 0821851357 |
This volume contains the proceedings of an AMS Special Session on Geometry, Physics, and Nonlinear PDEs, The conference brought together specialists in Monge-Ampere equations, prescribed curvature problems, mean curvature, harmonic maps, evolution with curvature-dependent speed, isospectral manifolds, and general relativity. An excellent overview of the frontiers of research in these areas.
Contact Geometry and Nonlinear Differential Equations
Title | Contact Geometry and Nonlinear Differential Equations PDF eBook |
Author | Alexei Kushner |
Publisher | Cambridge University Press |
Pages | 472 |
Release | 2007 |
Genre | Mathematics |
ISBN | 0521824761 |
Shows novel and modern ways of solving differential equations using methods from contact and symplectic geometry.
Geometry in Partial Differential Equations
Title | Geometry in Partial Differential Equations PDF eBook |
Author | Agostino Prastaro |
Publisher | World Scientific |
Pages | 482 |
Release | 1994 |
Genre | Mathematics |
ISBN | 9789810214074 |
This book emphasizes the interdisciplinary interaction in problems involving geometry and partial differential equations. It provides an attempt to follow certain threads that interconnect various approaches in the geometric applications and influence of partial differential equations. A few such approaches include: Morse-Palais-Smale theory in global variational calculus, general methods to obtain conservation laws for PDEs, structural investigation for the understanding of the meaning of quantum geometry in PDEs, extensions to super PDEs (formulated in the category of supermanifolds) of the geometrical methods just introduced for PDEs and the harmonic theory which proved to be very important especially after the appearance of the Atiyah-Singer index theorem, which provides a link between geometry and topology.
Geometry and Nonlinear Partial Differential Equations
Title | Geometry and Nonlinear Partial Differential Equations PDF eBook |
Author | Shing-Tung Yau |
Publisher | American Mathematical Soc. |
Pages | 250 |
Release | 2002 |
Genre | Mathematics |
ISBN | 0821832948 |
This book presents the proceedings of a conference on geometry and nonlinear partial differential equations dedicated to Professor Buqing Su in honor of his one-hundredth birthday. It offers a look at current research by Chinese mathematicians in differential geometry and geometric areas of mathematical physics. It is suitable for advanced graduate students and research mathematicians interested in geometry, topology, differential equations, and mathematical physics.