Included in series
North-Holland Mathematical Library, 69
Description
The 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.
Audience
Researchers and graduate students working in the field of partial
differential equations.
Contents
Introduction.
1. Preliminaries.
2. Integral inequalities.
3. The Laplace operator.
4. Strong solutions of the Dirichlet problem for linear equations.
5. The Dirichlet problem for elliptic linear.
divergent equations in a nonsmooth domain.
6. The Dirichlet problem for semilinear equations in a conical
domain.
7. Strong solutions of the Dirichlet problem for nondivergence
quasilinear equations.
8. Weak solutions of the Dirichlet problem for elliptic
divergence form quasilinear equations.
9. The behavior of weak solutions to the boundary value problems
for elliptic quasilinear equations with triple degeneration in a
neighborhood of a boundary edge.
10. Sharp estimates of solutions to the Robin.
boundary value problem for elliptic non divergence second order
equations in a neighborhood of the conical point.
Bibliography.
Notation Index.
Index.
Bibliographic & ordering Information
Hardbound, ISBN: 0-444-52109-7, 538 pages, publication date: 2006
Contents
Preface Outline of the Series Contents List of Contributors
Section 2C: Algebraic K-theory
Higher Algebraic K-theory (A. Kuku)
Section 3B: Associative Rings and Algebras
Filter Dimension (V.V. Bavula) Section 4E: Lie Algebras
Gelfand-Tsetlin Bases for Classical Lie Algebras (A.I. Molev)
Section 4H: Rings and Algebras with Additional Structure
Hopf Algebras (M. Cohen, S. Gelaki and S. Westreich) Difference
Algebra (A.B. Levin)
Section 5A: Groups and Semigroups
Reflection Groups (M. Geck and G. Malle) Hurwitz Groups and
Hurwitz Generation (M.C. Tamburini and M. Vsemirnov) Survey on
Braids (V. Vershinin) Groups with Finiteness Conditions (V.I.
Senashov)
Index
Bibliographic & ordering Information
Hardbound, ISBN: 0-444-52213-1, publication date: 2006
2006, XXII, 282 p. 110 illus., Hardcover
ISBN: 0-8176-3224-7
About this textbook
The congruences of a lattice form the congruence lattice. In the
past half-century, the study of congruence lattices has become a
large and important field with a great number of interesting and
deep results and many open problems. This self-contained
exposition by one of the leading experts in lattice theory,
George Gratzer, presents the major results on congruence lattices
of finite lattices featuring the author's signature "Proof-by-Picture"
method and its conversion to transparencies.
Key features:
* Includes the latest findings from a pioneering researcher in
the field
* Insightful discussion of techniques to construct "nice"
finite lattices with given congruence lattices and "nice"
congruence-preserving extensions
* Contains complete proofs, an extensive bibliography and index,
and nearly 80 open problems
* Additional information provided by the author online at:
http://www.maths.umanitoba.ca/homepages/gratzer.html/
The book is appropriate for a one-semester graduate course in
lattice theory, yet is also designed as a practical reference for
researchers studying lattices.
Table of contents
Series: Springer Monographs in Mathematics
1st ed. 1989. 2006, X, 338 p. 11 illus., Hardcover
ISBN: 3-540-29592-5
About this book
For the most part, this book is the translation from Japanese of
the earlier book written jointly by Koji Doi and the author who
revised it substantially for the English edition. It sets out to
provide the reader with the basic knowledge of elliptic modular
forms necessary to understand the recent developments in number
theory. The first part gives the general theory of modular
groups, modular forms and Hecke operators, with emphasis on the
Hecke-Weil theory of the relation between modular forms and
Dirichlet series. The second part is on the unit groups of
quaternion algebras, which are seldom dealt with in books. The so-called
Eichler-Selberg trace formula of Hecke operators follows next and
the explicit computable formula is given. In the last chapter,
written for the English edition, Eisenstein series with parameter
are discussed following the recent work of Shimura: Eisenstein
series are likely to play a very important role in the future
progress of number theory, and this chapter provides a good
introduction to the topic.
Table of contents
The Upper Half Plane and Fuchsian Groups.- Automorphic Forms.- L-Functions.-
Modular Groups and Modular Forms.- Unit Groups of Quaternion
Algebras.- Traces of Hecke Operators.- Eisenstein Series.
Series: Progress in Mathematical Physics, Vol. 47
2006, VIII, 293 p., Hardcover
ISBN: 3-7643-7435-7
About this book
The Poincare Seminar is held twice a year at the Institute Henri
Poincare in Paris. The goal of this seminar is to provide up-to-date
information about general topics of great interest in physics.
Both the theoretical and experimental results are covered, with
some historical background. Particular care is devoted to the
pedagogical nature of the presentation.
This volume is devoted to Einstein's 1905 papers and their legacy.
After a presentation of Einstein's epistemological approach to
physics, and the genesis of special relativity, a centenary
perspective is offered. The geometry of relativistic spacetime is
explained in detail. Single photon experiments are presented, as
a spectacular realization of Einstein's light quanta hypothesis.
A previously unpublished lecture by Einstein, which presents an
illuminating point of view on statistical physics in 1910, at the
dawn of quantum mechanics, is reproduced. The volume ends with an
essay on the historical, physical and mathematical aspects of
Brownian motion.
Table of contents