On the boundary behavior of solutions to a class of elliptic partial differential equations
Author: Kjell-Ove Widman
Publisher:
Published: 1966
Total Pages:
ISBN-13:
DOWNLOAD EBOOKPosts
The Boundary Behavior of Solutions of Quasilinear Second Order Elliptic Partial Differential Equations Arising from Geometrical Problems
Author: Chi-Ping Lau
Publisher:
Published: 1984
Total Pages: 224
ISBN-13:
DOWNLOAD EBOOKPartial Differential Equations and Boundary-Value Problems with Applications
Author: Mark A. Pinsky
Publisher: American Mathematical Soc.
Published: 2011
Total Pages: 545
ISBN-13: 0821868896
DOWNLOAD EBOOKBuilding on the basic techniques of separation of variables and Fourier series, the book presents the solution of boundary-value problems for basic partial differential equations: the heat equation, wave equation, and Laplace equation, considered in various standard coordinate systems--rectangular, cylindrical, and spherical. Each of the equations is derived in the three-dimensional context; the solutions are organized according to the geometry of the coordinate system, which makes the mathematics especially transparent. Bessel and Legendre functions are studied and used whenever appropriate throughout the text. The notions of steady-state solution of closely related stationary solutions are developed for the heat equation; applications to the study of heat flow in the earth are presented. The problem of the vibrating string is studied in detail both in the Fourier transform setting and from the viewpoint of the explicit representation (d'Alembert formula). Additional chapters include the numerical analysis of solutions and the method of Green's functions for solutions of partial differential equations. The exposition also includes asymptotic methods (Laplace transform and stationary phase). With more than 200 working examples and 700 exercises (more than 450 with answers), the book is suitable for an undergraduate course in partial differential equations.
Selected Works of Lipman Bers
Author: Lipman Bers
Publisher: American Mathematical Soc.
Published: 1998
Total Pages: 648
ISBN-13: 9780821809969
DOWNLOAD EBOOKHandbook of Differential Equations: Stationary Partial Differential Equations
Author: Michel Chipot
Publisher: Elsevier
Published: 2007-05-03
Total Pages: 627
ISBN-13: 0080521835
DOWNLOAD EBOOKA 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.- written by well-known experts in the field- self contained volume in series covering one of the most rapid developing topics in mathematics
Elliptic Boundary Value Problems of Second Order in Piecewise Smooth Domains
Author: Michail Borsuk
Publisher: Elsevier
Published: 2006-01-12
Total Pages: 538
ISBN-13: 0080461735
DOWNLOAD EBOOKThe book contains a systematic treatment of the qualitative theory of elliptic boundary value problems for linear and quasilinear second order equations in non-smooth domains. The authors concentrate on the following fundamental results: sharp estimates for strong and weak solutions, solvability of the boundary value problems, regularity assertions for solutions near singular points.Key features:* New the Hardy – Friedrichs – Wirtinger type inequalities as well as new integral inequalities related to the Cauchy problem for a differential equation.* Precise exponents of the solution decreasing rate near boundary singular points and best possible conditions for this.* The question about the influence of the coefficients smoothness on the regularity of solutions.* New existence theorems for the Dirichlet problem for linear and quasilinear equations in domains with conical points.* The precise power modulus of continuity at singular boundary point for solutions of the Dirichlet, mixed and the Robin problems.* The behaviour of weak solutions near conical point for the Dirichlet problem for m – Laplacian.* The behaviour of weak solutions near a boundary edge for the Dirichlet and mixed problem for elliptic quasilinear equations with triple degeneration.* Precise exponents of the solution decreasing rate near boundary singular points and best possible conditions for this.* The question about the influence of the coefficients smoothness on the regularity of solutions.* New existence theorems for the Dirichlet problem for linear and quasilinear equations in domains with conical points.* The precise power modulus of continuity at singular boundary point for solutions of the Dirichlet, mixed and the Robin problems.* The behaviour of weak solutions near conical point for the Dirichlet problem for m - Laplacian.* The behaviour of weak solutions near a boundary edge for the Dirichlet and mixed problem for elliptic quasilinear equations with triple degeneration.
Boundary Behavior of Holomorphic Functions of Several Complex Variables. (MN-11)
Author: Elias M. Stein
Publisher: Princeton University Press
Published: 2015-03-08
Total Pages: 83
ISBN-13: 1400871263
DOWNLOAD EBOOKThis book has as its subject the boundary value theory of holomorphic functions in several complex variables, a topic that is just now coming to the forefront of mathematical analysis. For one variable, the topic is classical and rather well understood. In several variables, the necessary understanding of holomorphic functions via partial differential equations has a recent origin, and Professor Stein's book, which emphasizes the potential-theoretic aspects of the boundary value problem, should become the standard work in the field. Originally published in 1972. The Princeton Legacy Library uses the latest print-on-demand technology to again make available previously out-of-print books from the distinguished backlist of Princeton University Press. These editions preserve the original texts of these important books while presenting them in durable paperback and hardcover editions. The goal of the Princeton Legacy Library is to vastly increase access to the rich scholarly heritage found in the thousands of books published by Princeton University Press since its founding in 1905.
Fine Regularity of Solutions of Elliptic Partial Differential Equations
Author: Jan Malý
Publisher: American Mathematical Soc.
Published: 1997
Total Pages: 309
ISBN-13: 0821803352
DOWNLOAD EBOOKThe primary objective of this monograph is to give a comprehensive exposition of results surrounding the work of the authors concerning boundary regularity of weak solutions of second order elliptic quasilinear equations in divergence form. The book also contains a complete development of regularity of solutions of variational inequalities, including the double obstacle problem, where the obstacles are allowed to be discontinuous. The book concludes with a chapter devoted to the existence theory thus providing the reader with a complete treatment of the subject ranging from regularity of weak solutions to the existence of weak solutions.
Explorations in Harmonic Analysis
Author: Steven G. Krantz
Publisher: Springer Science & Business Media
Published: 2009-05-24
Total Pages: 367
ISBN-13: 0817646698
DOWNLOAD EBOOKThis self-contained text provides an introduction to modern harmonic analysis in the context in which it is actually applied, in particular, through complex function theory and partial differential equations. It takes the novice mathematical reader from the rudiments of harmonic analysis (Fourier series) to the Fourier transform, pseudodifferential operators, and finally to Heisenberg analysis.
Partial Differential Equations
Author: Walter A. Strauss
Publisher: John Wiley & Sons
Published: 2007-12-21
Total Pages: 467
ISBN-13: 0470054565
DOWNLOAD EBOOKOur understanding of the fundamental processes of the natural world is based to a large extent on partial differential equations (PDEs). The second edition of Partial Differential Equations provides an introduction to the basic properties of PDEs and the ideas and techniques that have proven useful in analyzing them. It provides the student a broad perspective on the subject, illustrates the incredibly rich variety of phenomena encompassed by it, and imparts a working knowledge of the most important techniques of analysis of the solutions of the equations. In this book mathematical jargon is minimized. Our focus is on the three most classical PDEs: the wave, heat and Laplace equations. Advanced concepts are introduced frequently but with the least possible technicalities. The book is flexibly designed for juniors, seniors or beginning graduate students in science, engineering or mathematics.
