Series: Abel Symposia, Vol. 7
2012, 2012, X, 362 p. 31 illus., 11 in color.
Hardcover, ISBN 978-3-642-25360-7
Due: February 29, 2012
This area of mathematics is currently in the midst of an unprecedented development worldwide. Differential equations are used to model phenomena of increasing complexity, and in areas that have traditionally been outside the realm of mathematics. New analytical tools and numerical methods are dramatically improving our understanding of nonlinear models. Nonlinearity gives rise to novel effects reflected in the appearance of shock waves, turbulence, material defects, etc., and offer challenging novel mathematical problems. On the other hand, new mathematical developments provide new insight in many applications.
L.Ambrosio: Convergence of Wigner transforms in a semiclassical limit.- A.Bressan: Contractive Metrics for Nonsmooth Evolutions.- L. Caffarelli: Non local diffusions, drifts and games.- G.-Q.Chen and Y.G.Wang: Characteristic Discontinuities and Free Boundary Problems for Hyperbolic Conservation Laws.- S.Conti, C.De Lellis, L.Szekelyhidi Jr.: h-principle and rigidity for C1;a isometric embeddings.- J.Dolbeault, M.J.Esteban: About existence, symmetry and symmetry breaking for extremal functions of some interpolation functional inequalities.- E.Feireisl, M.E. Schonbek: On the Oberbeck?Boussinesq approximation on unbounded domains.- C.Kenig: Universal Profiles and Rigidity Theorems for the Energy Critical Wave Equation.- A.Kiselev, F.Nazarov: A simple energy pump for the surface quasi-geostrophic equation.- S.Klainerman: On the formation of trapped surfaces.- R.V.Kohn: Surface Relaxation Below the Roughening Temperature: Some Recent Progress and Open Questions.- A.J.Majda: Climate Science, Waves and PDEs for the Tropics.- I.Gallagher, T.Paul, L.Saint-Raymond: On the propagation of oceanic waves driven by a strong macroscopic flow.- E.Tadmor, C.Tan: Hierarchical construction of bounded solutions of divU = F in critical regularity spaces.- J.L.Vazquez: Nonlinear Diffusion with Fractional Laplacian Operators.- C.Villani: (Ir)reversibility and entropy?.
Series: Lecture Notes in Mathematics, Vol. 2044
2012, 2012, 246 p. 29 illus., 10 in color.
Softcover, ISBN 978-3-642-25982-1
Due: March 31, 2012
These notes provide an introduction to the theory of spherical harmonics in an arbitrary dimension as well as
an overview of classical and recent results on some aspects of the approximation of functions by spherical polynomials and numerical integration over the unit sphere. The notes are intended for graduate students in the mathematical sciences and researchers who are interested in solving problems involving partial differential and integral equations on the unit sphere, especially on the unit sphere in three-dimensional Euclidean space. Some related work for approximation on the unit disk in the plane is also briefly discussed, with results being generalizable to the unit ball in more dimensions.
Content Level ≫ Research
Keywords ≫ approximation theory - quadrature - spherical harmonic
Related subjects ≫ Analysis - Computational Science & Engineering - Dynamical Systems & Differential Equations - Physics
1 Preliminaries.- 2 Spherical Harmonics.- 3 Differentiation and Integration over the Sphere.- 4 Approximation Theory.- 5 Numerical Quadrature.- 6 Applications: Spectral Methods.
Series: Lecture Notes in Mathematics, Vol. 2045
Subseries: C.I.M.E. Foundation Subseries
2012, 2012, 256 p. 3 illus.
Softcover, ISBN 978-3-642-27144-1
Due: March 31, 2012
The issue of regularity has played a central role in the theory of Partial Differential Equations almost since its inception, and despite the tremendous advances made it still remains a very fruitful research field. In particular considerable strides have been made in regularity estimates for degenerate and singular elliptic and parabolic equations over the last several years, and in many unexpected and challenging directions.
Because of all these recent results, it seemed high time to create an overview that would highlight emerging trends and issues in this fascinating research topic in a proper and effective way.
The course aimed to show the deep connections between these topics and to open new research directions through the contributions of leading experts in all of these fields.
Content Level ≫ Research
Keywords ≫ 35J70, 35J75, 35J92, 35K65, 35K67, 35K86, 35K92, 49K20, 49N60 - Boundary Harnack Inequalities - Fractional Laplacian - Obstacle Problem - Random Tug-of-war Games - Supersolutions to degenerate parabolic equatons
Related subjects ≫ Dynamical Systems & Differential Equations - Mathematics
Applications of Boundary Harnack Inequalities for p Harmonic Functions and Related Topics.- Regularity of Supersolutions.- Introduction to random Tug-of-War games and PDEs.- The Problems of the Obstacle in Lower Dimension and for the Fractional Laplacian.
Series: Universitext
2012, 2012, XII, 328 p. 79 illus., 59 in color.
Softcover, ISBN 978-1-4614-2199-3
Due: April 28, 2012
Presents a precise and rigorous exposition of Stokes' theorem
Takes a differential geometric point of view on vector calculus and analysis
Designed as a textbook for upper-undergraduate students, and can also be useful for engineering and physics students?
The aim of this book is to facilitate the use of Stokes' Theorem in applications. The text takes a differential geometric point of view and provides for the student a bridge between pure and applied mathematics by carefully building a formal rigorous development of the topic and following this through to concrete applications in two and three variables. Several practical methods and many solved exercises are provided. This book tries to show that vector analysis and vector calculus are not always at odds with one another.
Key topics include:
-vectors and vector fields;
-line integrals;
-regular k-surfaces;
-flux of a vector field;
-orientation of a surface;
-differential forms;
-Stokes' theorem;
-divergence theorem.
This book is intended for upper undergraduate students who have completed a standard introduction to differential and integral calculus for functions of several variables. The book can also be useful to engineering and physics students who know how to handle the theorems of Green, Stokes and Gauss, but would like to explore the topic further.
Content Level ≫ Upper undergraduate
Preface.- 1 Vectors and Vector Fields.- 2 Line Integrals.- 3 Regular k-surfaces.- 4 Flux of a Vector Field.- 5 Orientation of a Surface.- 6 Differential Forms.- Integration on Surfaces.- 8 Surfaces with Boundary.- 9 The General Stokes' Theorem.- Solved Exercises?.- References.- Index
Series: Operator Theory: Advances and Applications, Vol. 221
2012, X, 742 p.
ISBN 978-3-0348-0296-3
Due: May 31, 2012
The present volume contains a collection of original research articles and expository contributions on recent developments in operator theory and its multifaceted applications. They cover a wide range of themes from the IWOTA 2010 conference held at the TU Berlin, Germany, including spectral theory, function spaces, mathematical system theory, evolution equations and semigroups, and differential and difference operators. The book encompasses new trends and various modern topics in operator theory, and serves as a useful source of information to mathematicians, scientists and engineers.
Content Level ≫ Research
Keywords ≫ differential and difference operators - evolution equations and semigroups - function spaces - mathematical system theory - spectral theory
Related subjects ≫ Analysis