Crack Theory And Edge Singularities

Author : D. V. Kapanadze,Bert-Wolfgang Schulze
Publisher : Springer Science & Business Media
Page : 512 pages
File Size : 41,8 Mb
Release : 2013-03-14
Category : Mathematics
ISBN : 9789401703239

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Crack Theory and Edge Singularities by D. V. Kapanadze,Bert-Wolfgang Schulze Pdf

Boundary value problems for partial differential equations playa crucial role in many areas of physics and the applied sciences. Interesting phenomena are often connected with geometric singularities, for instance, in mechanics. Elliptic operators in corresponding models are then sin gular or degenerate in a typical way. The necessary structures for constructing solutions belong to a particularly beautiful and ambitious part of the analysis. Cracks in a medium are described by hypersurfaces with a boundary. Config urations of that kind belong to the category of spaces (manifolds) with geometric singularities, here with edges. In recent years the analysis on such (in general, stratified) spaces has become a mathematical structure theory with many deep relations with geometry, topology, and mathematical physics. Key words in this connection are operator algebras, index theory, quantisation, and asymptotic analysis. Motivated by Lame's system with two-sided boundary conditions on a crack we ask the structure of solutions in weighted edge Sobolov spaces and subspaces with discrete and continuous asymptotics. Answers are given for elliptic sys tems in general. We construct parametrices of corresponding edge boundary value problems and obtain elliptic regularity in the respective scales of weighted spaces. The original elliptic operators as well as their parametrices belong to a block matrix algebra of pseudo-differential edge problems with boundary and edge conditions, satisfying analogues of the Shapiro-Lopatinskij condition from standard boundary value problems. Operators are controlled by a hierarchy of principal symbols with interior, boundary, and edge components.

Author : David Kapanadze
Publisher : Unknown
Page : 71 pages
File Size : 52,9 Mb
Release : 2001
Category : Electronic
ISBN : OCLC:722508178

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Crack Theory and Edge Singularities by David Kapanadze Pdf

Author : Michael Ruzhansky,Jens Wirth
Publisher : Springer Science & Business Media
Page : 366 pages
File Size : 54,6 Mb
Release : 2011-05-04
Category : Mathematics
ISBN : 9783034800693

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Modern Aspects of the Theory of Partial Differential Equations by Michael Ruzhansky,Jens Wirth Pdf

The book provides a quick overview of a wide range of active research areas in partial differential equations. The book can serve as a useful source of information to mathematicians, scientists and engineers. The volume contains contributions from authors from a large variety of countries on different aspects of partial differential equations, such as evolution equations and estimates for their solutions, control theory, inverse problems, nonlinear equations, elliptic theory on singular domains, numerical approaches.

Author : Pierre Albin,Dmitry Jakobson, Frédéric Rochon
Publisher : American Mathematical Soc.
Page : 378 pages
File Size : 45,7 Mb
Release : 2014-12-01
Category : Mathematics
ISBN : 9781470410438

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Geometric and Spectral Analysis by Pierre Albin,Dmitry Jakobson, Frédéric Rochon Pdf

In 2012, the Centre de Recherches Mathématiques was at the center of many interesting developments in geometric and spectral analysis, with a thematic program on Geometric Analysis and Spectral Theory followed by a thematic year on Moduli Spaces, Extremality and Global Invariants. This volume contains original contributions as well as useful survey articles of recent developments by participants from three of the workshops organized during these programs: Geometry of Eigenvalues and Eigenfunctions, held from June 4-8, 2012; Manifolds of Metrics and Probabilistic Methods in Geometry and Analysis, held from July 2-6, 2012; and Spectral Invariants on Non-compact and Singular Spaces, held from July 23-27, 2012. The topics covered in this volume include Fourier integral operators, eigenfunctions, probability and analysis on singular spaces, complex geometry, Kähler-Einstein metrics, analytic torsion, and Strichartz estimates. This book is co-published with the Centre de Recherches Mathématiques.

Author : M. W. Wong,Hongmei Zhu
Publisher : Birkhäuser
Page : 239 pages
File Size : 45,9 Mb
Release : 2017-01-20
Category : Mathematics
ISBN : 9783319475127

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Pseudo-Differential Operators: Groups, Geometry and Applications by M. W. Wong,Hongmei Zhu Pdf

This volume consists of papers inspired by the special session on pseudo-differential operators at the 10th ISAAC Congress held at the University of Macau, August 3-8, 2015 and the mini-symposium on pseudo-differential operators in industries and technologies at the 8th ICIAM held at the National Convention Center in Beijing, August 10-14, 2015. The twelve papers included present cutting-edge trends in pseudo-differential operators and applications from the perspectives of Lie groups (Chapters 1-2), geometry (Chapters 3-5) and applications (Chapters 6-12). Many contributions cover applications in probability, differential equations and time-frequency analysis. A focus on the synergies of pseudo-differential operators with applications, especially real-life applications, enhances understanding of the analysis and the usefulness of these operators.

Author : Ryuichi Ashino,Paolo Boggiatto,Man-Wah Wong
Publisher : Birkhäuser
Page : 236 pages
File Size : 54,9 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9783034878401

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Advances in Pseudo-Differential Operators by Ryuichi Ashino,Paolo Boggiatto,Man-Wah Wong Pdf

This volume consists of the plenary lectures and invited talks in the special session on pseudo-differential operators given at the Fourth Congress of the International Society for Analysis, Applications and Computation (ISAAC) held at York University in Toronto, August 11-16, 2003. The theme is to look at pseudo-differential operators in a very general sense and to report recent advances in a broad spectrum of topics, such as pde, quantization, filters and localization operators, modulation spaces, and numerical experiments in wavelet transforms and orthonormal wavelet bases.

Author : Luigi Rodino,Bert-Wolfgang Schulze,Man Wah Wong
Publisher : American Mathematical Soc.
Page : 432 pages
File Size : 47,7 Mb
Release : 2007-11-21
Category : Mathematics
ISBN : 0821871552

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Pseudo-differential Operators by Luigi Rodino,Bert-Wolfgang Schulze,Man Wah Wong Pdf

This volume is based on lectures given at the workshop on pseudo-differential operators held at the Fields Institute from December 11, 2006 to December 15, 2006. The two main themes of the workshop and hence this volume are partial differential equations and time-frequency analysis. The contents of this volume consist of five mini-courses for graduate students and post-docs, and fifteen papers on related topics. Of particular interest in this volume are the mathematical underpinnings, applications and ramifications of the relatively new Stockwell transform, which is a hybrid of the Gabor transform and the wavelet transform. The twenty papers in this volume reflect modern trends in the development of pseudo-differential operators.

Author : Mark Lʹvovich Agranovskiĭ
Publisher : American Mathematical Soc.
Page : 482 pages
File Size : 51,7 Mb
Release : 2008
Category : Mathematics
ISBN : 9780821841501

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Complex Analysis and Dynamical Systems III by Mark Lʹvovich Agranovskiĭ Pdf

The papers in this volume cover a wide variety of topics in the geometric theory of functions of one and several complex variables, including univalent functions, conformal and quasiconformal mappings, minimal surfaces, and dynamics in infinite-dimensional spaces. In addition, there are several articles dealing with various aspects of approximation theory and partial differential equations. Taken together, the articles collected here provide the reader with a panorama of activity in complex analysis, drawn by a number of leading figures in the field.

Author : Ram Shankar Pathak
Publisher : World Scientific
Page : 422 pages
File Size : 44,8 Mb
Release : 2001-05-23
Category : Mathematics
ISBN : 9789814542654

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Geometry, Analysis & Applications, Procs Of The Intl Conf by Ram Shankar Pathak Pdf

Geometrical concepts play a significant role in the analysis of physical systems. Apart from the intrinsic interest, the knowledge of differentiable manifolds has become useful — even mandatory — in an ever-increasing number of areas of mathematics and its applications. Many results/concepts in analysis find their most natural (generalized) setting in manifold theory. An interrelation of geometry and analysis can be found in this volume.The book presents original research, besides a few survey articles by eminent experts from all over the world on current trends of research in differential and algebraic geometry, classical and modern analysis including the theory of distributions (linear and nonlinear), partial differential equations and wavelets.

Author : Yuri I. Karlovich,Luigi Rodino,Bernd Silbermann,Ilya M. Spitkovsky
Publisher : Springer Science & Business Media
Page : 410 pages
File Size : 42,5 Mb
Release : 2012-10-30
Category : Mathematics
ISBN : 9783034805377

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Operator Theory, Pseudo-Differential Equations, and Mathematical Physics by Yuri I. Karlovich,Luigi Rodino,Bernd Silbermann,Ilya M. Spitkovsky Pdf

This volume is a collection of papers devoted to the 70th birthday of Professor Vladimir Rabinovich. The opening article (by Stefan Samko) includes a short biography of Vladimir Rabinovich, along with some personal recollections and bibliography of his work. It is followed by twenty research and survey papers in various branches of analysis (pseudodifferential operators and partial differential equations, Toeplitz, Hankel, and convolution type operators, variable Lebesgue spaces, etc.) close to Professor Rabinovich's research interests. Many of them are written by participants of the International workshop “Analysis, Operator Theory, and Mathematical Physics” (Ixtapa, Mexico, January 23–27, 2012) having a long history of scientific collaboration with Vladimir Rabinovich, and are partially based on the talks presented there.The volume will be of great interest to researchers and graduate students in differential equations, operator theory, functional and harmonic analysis, and mathematical physics.​

Author : Gohar Harutyunyan,Bert-Wolfgang Schulze
Publisher : European Mathematical Society
Page : 782 pages
File Size : 45,7 Mb
Release : 2007
Category : Mathematics
ISBN : 303719040X

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Elliptic Mixed, Transmission and Singular Crack Problems by Gohar Harutyunyan,Bert-Wolfgang Schulze Pdf

Mixed, transmission, or crack problems belong to the analysis of boundary value problems on manifolds with singularities. The Zaremba problem with a jump between Dirichlet and Neumann conditions along an interface on the boundary is a classical example. The central theme of this book is to study mixed problems in standard Sobolev spaces as well as in weighted edge spaces where the interfaces are interpreted as edges. Parametrices and regularity of solutions are obtained within a systematic calculus of boundary value problems on manifolds with conical or edge singularities. This calculus allows singularities on the interface and homotopies between mixed and crack problems. Additional edge conditions are computed in terms of relative index results. In a detailed final chapter, the intuitive ideas of the approach are illustrated, and there is a discussion of future challenges. A special feature of the text is the inclusion of many worked-out examples which help the reader to appreciate the scope of the theory and to treat new cases of practical interest. This book is addressed to mathematicians and physicists interested in models with singularities, associated boundary value problems, and their solvability strategies based on pseudo-differential operators. The material is also useful for students in higher semesters and young researchers, as well as for experienced specialists working in analysis on manifolds with geometric singularities, the applications of index theory and spectral theory, operator algebras with symbolic structures, quantisation, and asymptotic analysis.

Author : Luigi Rodino,M. W. Wong,Hongmei Zhu
Publisher : Springer Science & Business Media
Page : 308 pages
File Size : 54,9 Mb
Release : 2011-03-14
Category : Mathematics
ISBN : 9783034800495

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Pseudo-Differential Operators: Analysis, Applications and Computations by Luigi Rodino,M. W. Wong,Hongmei Zhu Pdf

This volume consists of eighteen peer-reviewed papers related to lectures on pseudo-differential operators presented at the meeting of the ISAAC Group in Pseudo-Differential Operators (IGPDO) held at Imperial College London on July 13-18, 2009. Featured in this volume are the analysis, applications and computations of pseudo-differential operators in mathematics, physics and signal analysis. This volume is a useful complement to the volumes “Advances in Pseudo-Differential Operators”, “Pseudo-Differential Operators and Related Topics”, “Modern Trends in Pseudo-Differential Operators”, “New Developments in Pseudo-Differential Operators” and “Pseudo-Differential Operators: Complex Analysis and Partial Differential Equations” published in the same series in, respectively, 2004, 2006, 2007, 2009 and 2010.

Author : Joachim Escher,Elmar Schrohe,Jörg Seiler,Christoph Walker
Publisher : Springer
Page : 291 pages
File Size : 49,6 Mb
Release : 2015-06-04
Category : Mathematics
ISBN : 9783319125473

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Elliptic and Parabolic Equations by Joachim Escher,Elmar Schrohe,Jörg Seiler,Christoph Walker Pdf

The international workshop on which this proceedings volume is based on brought together leading researchers in the field of elliptic and parabolic equations. Particular emphasis was put on the interaction between well-established scientists and emerging young mathematicians, as well as on exploring new connections between pure and applied mathematics. The volume contains material derived after the workshop taking up the impetus to continue collaboration and to incorporate additional new results and insights.

Author : Shahla Molahajloo,Stevan Pilipović,Joachim Toft,M. W. Wong
Publisher : Springer Science & Business Media
Page : 370 pages
File Size : 51,7 Mb
Release : 2013-02-26
Category : Mathematics
ISBN : 9783034805858

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Pseudo-Differential Operators, Generalized Functions and Asymptotics by Shahla Molahajloo,Stevan Pilipović,Joachim Toft,M. W. Wong Pdf

This volume consists of twenty peer-reviewed papers from the special session on pseudodifferential operators and the special session on generalized functions and asymptotics at the Eighth Congress of ISAAC held at the Peoples’ Friendship University of Russia in Moscow on August 22‒27, 2011. The category of papers on pseudo-differential operators contains such topics as elliptic operators assigned to diffeomorphisms of smooth manifolds, analysis on singular manifolds with edges, heat kernels and Green functions of sub-Laplacians on the Heisenberg group and Lie groups with more complexities than but closely related to the Heisenberg group, Lp-boundedness of pseudo-differential operators on the torus, and pseudo-differential operators related to time-frequency analysis. The second group of papers contains various classes of distributions and algebras of generalized functions with applications in linear and nonlinear differential equations, initial value problems and boundary value problems, stochastic and Malliavin-type differential equations. This second group of papers are related to the third collection of papers via the setting of Colombeau-type spaces and algebras in which microlocal analysis is developed by means of techniques in asymptotics. The volume contains the synergies of the three areas treated and is a useful complement to volumes 155, 164, 172, 189, 205 and 213 published in the same series in, respectively, 2004, 2006, 2007, 2009, 2010 and 2011.

Author : Juan Gil,Thomas Krainer,Ingo Witt
Publisher : Birkhäuser
Page : 574 pages
File Size : 49,9 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9783034878500

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Aspects of Boundary Problems in Analysis and Geometry by Juan Gil,Thomas Krainer,Ingo Witt Pdf

Boundary problems constitute an essential field of common mathematical interest, they lie in the center of research activities both in analysis and geometry. This book encompasses material from both disciplines, and focuses on their interactions which are particularly apparent in this field. Moreover, the survey style of the contributions makes the topics accessible to a broad audience with a background in analysis or geometry, and enables the reader to get a quick overview.