Thomas Alazard – författare
474 kr
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840 kr
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Through 65 fully solved problems, the book offers readers a fast but in-depth introduction to the field, covering advanced topics in microlocal analysis, including pseudo- and para-differential calculus, and the key classical equations, such as the Laplace, Schrödinger or Navier-Stokes equations. Essentially self-contained, the book begins with problems on the necessary tools from functional analysis, distributions, and the theory of functional spaces, and in each chapter the problems are preceded by a summary of the relevant results of the theory.
Informed by the authors'' extensive research experience and years of teaching, this book is for graduate students and researchers who wish to gain real working knowledge of the subject.
Free Boundary Problems in Fluid Dynamics
600 kr
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764 kr
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This book, originating from a seminar held at Oberwolfach in 2022, introduces to state-of-the-art methods and results in the study of free boundary problems which are arising from compressible as well as from incompressible Euler’s equations in general. A particular set of such problems is given by gaseous stars considered in a vacuum (modeled via the compressible Euler equations) as well as water waves in their full generality (seen as recasts of incompressible irrotational Euler equations). This is a broad research area which is highly relevant to many real life problems, and in which substantial progress has been made in the last decade.
657 kr
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870 kr
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This textbook provides a modern introduction to advanced concepts and methods of mathematical analysis.
The first three parts of the book cover functional analysis, harmonic analysis, and microlocal analysis. Each chapter is designed to provide readers with a solid understanding of fundamental concepts while guiding them through detailed proofs of significant theorems. These include the universal approximation property for artificial neural networks, Brouwer''s domain invariance theorem, Nash''s implicit function theorem, Calderón''s reconstruction formula and wavelets, Wiener''s Tauberian theorem, Hörmander''s theorem of propagation of singularities, and proofs of many inequalities centered around the works of Hardy, Littlewood, and Sobolev. The final part of the book offers an overview of the analysis of partial differential equations. This vast subject is approached through a selection of major theorems such as the solution to Calderón''s problem, De Giorgi''s regularity theorem for elliptic equations, and the proof of a Strichartz–Bourgain estimate. Several renowned results are included in the numerous examples.
Based on courses given successively at the École Normale Supérieure in France (ENS Paris and ENS Paris-Saclay) and at Tsinghua University, the book is ideally suited for graduate courses in analysis and PDE. The prerequisites in topology and real analysis are conveniently recalled in the appendix