Degenerate Elliptic Equations PDF Download
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Author: Serge Levendorskii
Publisher: Springer Science & Business Media
ISBN: 9401712158
Category : Mathematics
Languages : en
Pages : 442
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Book Description
This volume is the first to be devoted to the study of various properties of wide classes of degenerate elliptic operators of arbitrary order and pseudo-differential operators with multiple characteristics. Conditions for operators to be Fredholm in appropriate weighted Sobolev spaces are given, a priori estimates of solutions are derived, inequalities of the Grding type are proved, and the principal term of the spectral asymptotics for self-adjoint operators is computed. A generalization of the classical Weyl formula is proposed. Some results are new, even for operators of the second order. In addition, an analogue of the Boutet de Monvel calculus is developed and the index is computed. For postgraduate and research mathematicians, physicists and engineers whose work involves the solution of partial differential equations.
Author: Serge Levendorskii
Publisher: Springer Science & Business Media
ISBN: 9401712158
Category : Mathematics
Languages : en
Pages : 442
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Book Description
This volume is the first to be devoted to the study of various properties of wide classes of degenerate elliptic operators of arbitrary order and pseudo-differential operators with multiple characteristics. Conditions for operators to be Fredholm in appropriate weighted Sobolev spaces are given, a priori estimates of solutions are derived, inequalities of the Grding type are proved, and the principal term of the spectral asymptotics for self-adjoint operators is computed. A generalization of the classical Weyl formula is proposed. Some results are new, even for operators of the second order. In addition, an analogue of the Boutet de Monvel calculus is developed and the index is computed. For postgraduate and research mathematicians, physicists and engineers whose work involves the solution of partial differential equations.
Author: Juha Heinonen
Publisher: Courier Dover Publications
ISBN: 0486830462
Category : Mathematics
Languages : en
Pages : 417
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Book Description
A self-contained treatment appropriate for advanced undergraduates and graduate students, this text offers a detailed development of the necessary background for its survey of the nonlinear potential theory of superharmonic functions. 1993 edition.
Author: Maria Colombo
Publisher: Springer
ISBN: 8876426078
Category : Mathematics
Languages : en
Pages : 285
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Book Description
The first part of the book is devoted to the transport equation for a given vector field, exploiting the lagrangian structure of solutions. It also treats the regularity of solutions of some degenerate elliptic equations, which appear in the eulerian counterpart of some transport models with congestion. The second part of the book deals with the lagrangian structure of solutions of the Vlasov-Poisson system, which describes the evolution of a system of particles under the self-induced gravitational/electrostatic field, and the existence of solutions of the semigeostrophic system, used in meteorology to describe the motion of large-scale oceanic/atmospheric flows.
Author: Luis A. Caffarelli
Publisher: American Mathematical Soc.
ISBN: 0821804375
Category : Mathematics
Languages : en
Pages : 114
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Book Description
The goal of the book is to extend classical regularity theorems for solutions of linear elliptic partial differential equations to the context of fully nonlinear elliptic equations. This class of equations often arises in control theory, optimization, and other applications. The authors give a detailed presentation of all the necessary techniques. Instead of treating these techniques in their greatest generality, they outline the key ideas and prove the results needed for developing the subsequent theory. Topics discussed in the book include the theory of viscosity solutions for nonlinear equations, the Alexandroff estimate and Krylov-Safonov Harnack-type inequality for viscosity solutions, uniqueness theory for viscosity solutions, Evans and Krylov regularity theory for convex fully nonlinear equations, and regularity theory for fully nonlinear equations with variable coefficients.
Author: E.W. Stredulinsky
Publisher: Springer
ISBN: 3540389288
Category : Mathematics
Languages : en
Pages : 149
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Book Description
Author: Qiujun Zhang
Publisher:
ISBN:
Category : Boundary value problems
Languages : en
Pages : 56
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Book Description
Author: Albo Carlos Cavalheiro
Publisher: Cambridge Scholars Publishing
ISBN: 1527551679
Category : Mathematics
Languages : en
Pages : 333
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Book Description
In various applications, we can meet boundary value problems for elliptic equations whose ellipticity is disturbed in the sense that some degeneration or singularity appears. This bad behavior can be caused by the coefficients of the corresponding differential operator as well as by the solution itself. There are several very concrete problems in various practices which lead to such differential equations, such as glaciology, non-Newtonian fluid mechanics, flows through porous media, differential geometry, celestial mechanics, climatology, and reaction-diffusion problems, among others. This book is based on research by the author on degenerate elliptic equations. This book will be a useful reference source for graduate students and researchers interested in differential equations.
Author: Albo Carlos Cavalheiro
Publisher:
ISBN: 9783659818301
Category :
Languages : en
Pages : 252
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Book Description
Author: Jingyi Chen
Publisher: Springer Nature
ISBN: 3030349535
Category : Mathematics
Languages : en
Pages : 616
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Book Description
This edited volume has a two-fold purpose. First, comprehensive survey articles provide a way for beginners to ease into the corresponding sub-fields. These are then supplemented by original works that give the more advanced readers a glimpse of the current research in geometric analysis and related PDEs. The book is of significant interest for researchers, including advanced Ph.D. students, working in geometric analysis. Readers who have a secondary interest in geometric analysis will benefit from the survey articles. The results included in this book will stimulate further advances in the subjects: geometric analysis, including complex differential geometry, symplectic geometry, PDEs with a geometric origin, and geometry related to topology. Contributions by Claudio Arezzo, Alberto Della Vedova, Werner Ballmann, Henrik Matthiesen, Panagiotis Polymerakis, Sun-Yung A. Chang, Zheng-Chao Han, Paul Yang, Tobias Holck Colding, William P. Minicozzi II, Panagiotis Dimakis, Richard Melrose, Akito Futaki, Hajime Ono, Jiyuan Han, Jeff A. Viaclovsky, Bruce Kleiner, John Lott, Sławomir Kołodziej, Ngoc Cuong Nguyen, Chi Li, Yuchen Liu, Chenyang Xu, YanYan Li, Luc Nguyen, Bo Wang, Shiguang Ma, Jie Qing, Xiaonan Ma, Sean Timothy Paul, Kyriakos Sergiou, Tristan Rivière, Yanir A. Rubinstein, Natasa Sesum, Jian Song, Jeffrey Streets, Neil S. Trudinger, Yu Yuan, Weiping Zhang, Xiaohua Zhu and Aleksey Zinger.
Author: Marino Badiale
Publisher: Springer Science & Business Media
ISBN: 0857292277
Category : Mathematics
Languages : en
Pages : 204
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Book Description
Semilinear elliptic equations are of fundamental importance for the study of geometry, physics, mechanics, engineering and life sciences. The variational approach to these equations has experienced spectacular success in recent years, reaching a high level of complexity and refinement, with a multitude of applications. Additionally, some of the simplest variational methods are evolving as classical tools in the field of nonlinear differential equations. This book is an introduction to variational methods and their applications to semilinear elliptic problems. Providing a comprehensive overview on the subject, this book will support both student and teacher engaged in a first course in nonlinear elliptic equations. The material is introduced gradually, and in some cases redundancy is added to stress the fundamental steps in theory-building. Topics include differential calculus for functionals, linear theory, and existence theorems by minimization techniques and min-max procedures. Requiring a basic knowledge of Analysis, Functional Analysis and the most common function spaces, such as Lebesgue and Sobolev spaces, this book will be of primary use to graduate students based in the field of nonlinear partial differential equations. It will also serve as valuable reading for final year undergraduates seeking to learn about basic working tools from variational methods and the management of certain types of nonlinear problems.
