FUNCT SPAC PART DIFF EQUAT V2 OLSMA C

Erscheinungsjahr 2015
ISBN: 978-0-19-873315-7
Verlag: ACADEMIC

Buch, Englisch, 480 Seiten, Format (B × H): 161 mm x 240 mm, Gewicht: 881 g

This is a book written primarily for graduate students and early researchers in the fields of Analysis and Partial Differential Equations (PDEs). Coverage of the material is essentially self-contained, extensive and novel with great attention to details and rigour. The strength of the book primarily lies in its clear and detailed explanations, scope and coverage, highlighting and presenting deep and profound inter-connections between different related and seemingly unrelated disciplines within classical and modern mathematics and above all the extensive collection of examples, worked-out and hinted exercises. There are well over 700 exercises of varying level leading the reader from the basics to the most advanced levels and frontiers of research. The book can be used either for independent study or for a year-long graduate level course. In fact it has its origin in a year-long graduate course taught by the author in Oxford in 2004-5 and various parts of it in other institutions later on. A good number of distinguished researchers and faculty in mathematics worldwide have started their research career from the course that formed the basis for this book.

Autoren/Hrsg.

Taheri

Taheri, Ali

Fachgebiete

• Naturwissenschaften Physik Physik Allgemein Theoretische Physik, Mathematische Physik, Computerphysik
• Mathematik | Informatik Mathematik Mathematik Allgemein
• Mathematik | Informatik Mathematik Mathematische Analysis Moderne Anwendungen der Analysis

Inhaltsverzeichnis

- 13: Maximal Function; Bounding Averages and Pointwise Convergence

- 14: Harmonic-Hardy Spaces hp(H)

- 15: Sobolev Spaces; A Resolution of the Dirichlet Principle

- 16: Singular Integral Operators and Vector-Valued Inequalities

- 17: Littlewood-Paley Theory, Lp-Multipliers and Function Spaces

- 18: Morrey and Campanato vs. Hardy and John-Nirenberg Spaces

- 19: Layered Potentials, Jump Relations and Existence Theorems

- 20: Second Order Equations in Divergence Form: Continuous Coefficients

- 21: Second Order Equations in Divergence Form: Measurable Coefficients

- A: Partition of Unity

- B: Total Boundedness and Compact Subsets of Lp

- C: Gamma and Beta Functions

- D: Volume of the Unit n-Ball

- E: Integrals Related to Abel and Gauss Kernels

- F: Hausdorff Measures Hs

- G: Evaluation of Some Integrals Over

- H: Sobolev Spaces

Über Autor(innen)

Dr Taheri is a Reader in Mathematics as the University of Sussex. His primary research area is in the field of years. During which time he has published research papers in prestigious journals, made valuable contributions to the field and has taught and conducted research in some of the leading institutions in the world including Oxford, Courant Institute, Max-Planck-Institute Leipzig and Warwick. He heads up the Analysis and PDEs research group in Sussex In June 2014 he was awarded the First University of Sussex Student Led Teaching Prize for "Outstanding and Innovative Postgraduate Teaching in Mathematics".