Lectures on Linear Partial Differential Equations
- ISBN-10
- 0821852841
- ISBN-13
- 9780821852842
- Category
- Differential equations, Elliptic
- Pages
- 410
- Language
- English
- Published
- 2011
- Publisher
- American Mathematical Soc.
- Author
- Grigoriĭ Ilʹich Eskin
Description
This book is a reader-friendly, relatively short introduction to the modern theory of linear partial differential equations. An effort has been made to present complete proofs in an accessible and self-contained form. The first three chapters are on elementary distribution theory and Sobolev spaces with many examples and applications to equations with constant coefficients. The following chapters study the Cauchy problem for parabolic and hyperbolic equations, boundary value problems for elliptic equations, heat trace asymptotics, and scattering theory. The book also covers microlocal analysis, including the theory of pseudodifferential and Fourier integral operators, and the propagation of singularities for operators of real principal type. Among the more advanced topics are the global theory of Fourier integral operators and the geometric optics construction in the large, the Atiyah-Singer index theorem in $\mathbb R^n$, and the oblique derivative problem.
Get the book
Other editions
Similar books
-
First Order Elliptic Systems: A Function Theoretic Approach
By Robert P. Gilbert, James L. BuchananFirst Order Elliptic Systems: A Function Theoretic Approach
-
Fully Nonlinear Elliptic Equations
By Luis A. Caffarelli, Xavier CabréThe 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.
-
Elliptic Partial Differential Equations
By Qing Han, Fanghua LinThis volume is based on PDE courses given by the authors at the Courant Institute and at the University of Notre Dame, Indiana.
-
Second Order Elliptic Equations and Elliptic Systems
By Ya-Zhe Chen, Lan-Cheng WuThe book features appropriate materials and is an excellent textbook for graduate students. The volume is also useful as a reference source for undergraduate mathematics majors, graduate students, professors, and scientists.
-
Qualitative Analysis of Nonlinear Elliptic Partial Differential Equations: Monotonicity, Analytic, and Variational Methods
By Vicenţiu D. RădulescuThis book provides a comprehensive introduction to the mathematical theory of nonlinear problems described by elliptic partial differential equations.
-
Nonlinear Functional Analysis and Applications to Differential Equations: Proceedings of the Second School, ICTP, Trieste, Italy, 21 April-9 May 1997
By Antonio AmbrosettiRecent results for asymmetric nonlinear boundary value problems / D. Arcoya -- Connecting orbits of Hamiltonian systems / S.V. Bolotin -- Morse theory in nonlinear analysis / K.-C. Chang -- Critical point theory and applications to elliptic ...
-
Second Order Elliptic Equations and Elliptic Systems
By Yazhe ChenSecond Order Elliptic Equations and Elliptic Systems
-
Nonlinear Elliptic Partial Differential Equations: Workshop in Celebration of Jean-Pierre Gossez's 65th Birthday, September 2-4, 2009, Université Libre de Bruxelles,...
By Denis Bonheure, J. P. Gossez... Conformally invariant powers of the Laplacian. I. Existence. J. London Math. Soc. 46, (1992), 557-565. [16] Graham, C.R; Zworski, M. Scattering matrix in conformal geometry. Invent. Math. 152, (2003), no. 1, 89-118. [17] Hamilton, R.S. ...
-
Qualitative Analysis of Nonlinear Elliptic Partial Differential Equations
This book provides a comprehensive introduction to the mathematical theory of nonlinear problems described by elliptic partial differential equations.
-
PLTMG, a Software Package for Solving Elliptic Partial Differential Equations: Users' Guide 8.0
By Randolph E. BankIntended mainly for use as a reference manual, this edition encompasses all the improvements of the newest version of the PLTMG software package. This updated version introduces several significant changes.