Download or read book Square Root Problem for Divergence Operators and Related Topics written by Pascal Auscher and published by . This book was released on 1998 with total page 190 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Harmonic Analysis and Boundary Value Problems written by Luca Capogna and published by American Mathematical Soc.. This book was released on 2001 with total page 170 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume presents research and expository articles by the participants of the 25th Arkansas Spring Lecture Series on ``Recent Progress in the Study of Harmonic Measure from a Geometric and Analytic Point of View'' held at the University of Arkansas (Fayetteville). Papers in this volume provide clear and concise presentations of many problems that are at the forefront of harmonic analysis and partial differential equations. The following topics are featured: the solution of the Kato conjecture, the ``two bricks'' problem, new results on Cauchy integrals on non-smooth curves, the Neumann problem for sub-Laplacians, and a new general approach to both divergence and nondivergence second order parabolic equations based on growth theorems. The articles in this volume offer both students and researchers a comprehensive volume of current results in the field.
Download or read book Sobolev Spaces Their Generalizations and Elliptic Problems in Smooth and Lipschitz Domains written by Mikhail S. Agranovich and published by Springer. This book was released on 2015-05-06 with total page 343 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book, which is based on several courses of lectures given by the author at the Independent University of Moscow, is devoted to Sobolev-type spaces and boundary value problems for linear elliptic partial differential equations. Its main focus is on problems in non-smooth (Lipschitz) domains for strongly elliptic systems. The author, who is a prominent expert in the theory of linear partial differential equations, spectral theory and pseudodifferential operators, has included his own very recent findings in the present book. The book is well suited as a modern graduate textbook, utilizing a thorough and clear format that strikes a good balance between the choice of material and the style of exposition. It can be used both as an introduction to recent advances in elliptic equations and boundary value problems and as a valuable survey and reference work. It also includes a good deal of new and extremely useful material not available in standard textbooks to date. Graduate and post-graduate students, as well as specialists working in the fields of partial differential equations, functional analysis, operator theory and mathematical physics will find this book particularly valuable.
Download or read book Harmonic Analysis and Partial Differential Equations written by Patricio Cifuentes and published by American Mathematical Soc.. This book was released on 2010-01-14 with total page 258 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains the Proceedings of the 8th International Conference on Harmonic Analysis and Partial Differential Equations, held in El Escorial, Madrid, Spain, on June 16-20, 2008. Featured in this book are papers by Steve Hoffmann and Carlos Kenig, which are based on two mini-courses given at the conference. These papers present topics of current interest, which assume minimal background from the reader, and represent state-of-the-art research in a useful way for young researchers. Other papers in this volume cover a range of fields in Harmonic Analysis and Partial Differential Equations and, in particular, illustrate well the fruitful interplay between these two fields.
Download or read book Harmonic Analysis Partial Differential Equations Complex Analysis Banach Spaces and Operator Theory Volume 1 written by María Cristina Pereyra and published by Springer. This book was released on 2016-09-15 with total page 380 pages. Available in PDF, EPUB and Kindle. Book excerpt: Covering a range of subjects from operator theory and classical harmonic analysis to Banach space theory, this book contains survey and expository articles by leading experts in their corresponding fields, and features fully-refereed, high-quality papers exploring new results and trends in spectral theory, mathematical physics, geometric function theory, and partial differential equations. Graduate students and researchers in analysis will find inspiration in the articles collected in this volume, which emphasize the remarkable connections between harmonic analysis and operator theory. Another shared research interest of the contributors of this volume lies in the area of applied harmonic analysis, where a new notion called chromatic derivatives has recently been introduced in communication engineering. The material for this volume is based on the 13th New Mexico Analysis Seminar held at the University of New Mexico, April 3-4, 2014 and on several special sections of the Western Spring Sectional Meeting at the University of New Mexico, April 4-6, 2014. During the event, participants honored the memory of Cora Sadosky—a great mathematician who recently passed away and who made significant contributions to the field of harmonic analysis. Cora was an exceptional mathematician and human being. She was a world expert in harmonic analysis and operator theory, publishing over fifty-five research papers and authoring a major textbook in the field. Participants of the conference include new and senior researchers, recent doctorates as well as leading experts in the area.
Download or read book Perspectives in Partial Differential Equations Harmonic Analysis and Applications written by Dorina Mitrea and published by American Mathematical Soc.. This book was released on 2008 with total page 446 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains a collection of papers contributed on the occasion of Mazya's 70th birthday by a distinguished group of experts of international stature in the fields of harmonic analysis, partial differential equations, function theory, and spectral analysis, reflecting the state of the art in these areas.
Download or read book The Functional Calculus for Sectorial Operators written by Markus Haase and published by Springer Science & Business Media. This book was released on 2006-08-18 with total page 399 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book contains a systematic and partly axiomatic treatment of the holomorphic functional calculus for unbounded sectorial operators. The account is generic so that it can be used to construct and interrelate holomorphic functional calculi for other types of unbounded operators. Particularly, an elegant unified approach to holomorphic semigroups is obtained. The last chapter describes applications to PDE, evolution equations and approximation theory as well as the connection with harmonic analysis.
Download or read book Elliptic Partial Differential Equations with Almost Real Coefficients written by Ariel Barton and published by American Mathematical Soc.. This book was released on 2013-04-22 with total page 120 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this monograph the author investigates divergence-form elliptic partial differential equations in two-dimensional Lipschitz domains whose coefficient matrices have small (but possibly nonzero) imaginary parts and depend only on one of the two coordinates. He shows that for such operators, the Dirichlet problem with boundary data in $L^q$ can be solved for $q1$ small enough, and provide an endpoint result at $p=1$.
Download or read book Boundary Value Problems and Hardy Spaces for Elliptic Systems with Block Structure written by Pascal Auscher and published by Springer Nature. This book was released on 2023-08-28 with total page 310 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this monograph, for elliptic systems with block structure in the upper half-space and t-independent coefficients, the authors settle the study of boundary value problems by proving compatible well-posedness of Dirichlet, regularity and Neumann problems in optimal ranges of exponents. Prior to this work, only the two-dimensional situation was fully understood. In higher dimensions, partial results for existence in smaller ranges of exponents and for a subclass of such systems had been established. The presented uniqueness results are completely new, and the authors also elucidate optimal ranges for problems with fractional regularity data. The first part of the monograph, which can be read independently, provides optimal ranges of exponents for functional calculus and adapted Hardy spaces for the associated boundary operator. Methods use and improve, with new results, all the machinery developed over the last two decades to study such problems: the Kato square root estimates and Riesz transforms, Hardy spaces associated to operators, off-diagonal estimates, non-tangential estimates and square functions, and abstract layer potentials to replace fundamental solutions in the absence of local regularity of solutions.
Download or read book Handbook of Differential Equations Evolutionary Equations written by C.M. Dafermos and published by Elsevier. This book was released on 2004-08-24 with total page 579 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book contains several introductory texts concerning the main directions in the theory of evolutionary partial differential equations. The main objective is to present clear, rigorous,and in depth surveys on the most important aspects of the present theory. The table of contents includes: W.Arendt: Semigroups and evolution equations: Calculus, regularity and kernel estimatesA.Bressan: The front tracking method for systems of conservation lawsE.DiBenedetto, J.M.Urbano,V.Vespri: Current issues on singular and degenerate evolution equations;L.Hsiao, S.Jiang: Nonlinear hyperbolic-parabolic coupled systemsA.Lunardi: Nonlinear parabolic equations and systemsD.Serre:L1-stability of nonlinear waves in scalar conservation laws B.Perthame:Kinetic formulations of parabolic and hyperbolic PDE's: from theory to numerics
Download or read book Nonlinear Elliptic and Parabolic Problems written by Michel Chipot and published by Springer Science & Business Media. This book was released on 2006-02-09 with total page 531 pages. Available in PDF, EPUB and Kindle. Book excerpt: Celebrates the work of the renowned mathematician Herbert Amann, who had a significant and decisive influence in shaping Nonlinear Analysis. Containing 32 contributions, this volume covers a range of nonlinear elliptic and parabolic equations, with applications to natural sciences and engineering.
Download or read book Partial Differential Equations and Functional Analysis written by Erik Koelink and published by Springer Science & Business Media. This book was released on 2006-08-18 with total page 294 pages. Available in PDF, EPUB and Kindle. Book excerpt: Capturing the state of the art of the interplay between partial differential equations, functional analysis, maximal regularity, and probability theory, this volume was initiated at the Delft conference on the occasion of the retirement of Philippe Clément. It will be of interest to researchers in PDEs and functional analysis.
Download or read book Functional Analytic Methods for Evolution Equations written by Giuseppe Da Prato and published by Springer. This book was released on 2004-08-30 with total page 478 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book consists of five introductory contributions by leading mathematicians on the functional analytic treatment of evolutions equations. In particular the contributions deal with Markov semigroups, maximal L^p-regularity, optimal control problems for boundary and point control systems, parabolic moving boundary problems and parabolic nonautonomous evolution equations. The book is addressed to PhD students, young researchers and mathematicians doing research in one of the above topics.
Download or read book Analysis of Pseudo Differential Operators written by Shahla Molahajloo and published by Springer. This book was released on 2019-05-08 with total page 259 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume, like its predecessors, is based on the special session on pseudo-differential operators, one of the many special sessions at the 11th ISAAC Congress, held at Linnaeus University in Sweden on August 14-18, 2017. It includes research papers presented at the session and invited papers by experts in fields that involve pseudo-differential operators. The first four chapters focus on the functional analysis of pseudo-differential operators on a spectrum of settings from Z to Rn to compact groups. Chapters 5 and 6 discuss operators on Lie groups and manifolds with edge, while the following two chapters cover topics related to probabilities. The final chapters then address topics in differential equations.
Download or read book Concrete Operators Spectral Theory Operators in Harmonic Analysis and Approximation written by Manuel Cepedello Boiso and published by Springer Science & Business Media. This book was released on 2013-11-04 with total page 546 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book contains a collection of research articles and surveys on recent developments on operator theory as well as its applications covered in the IWOTA 2011 conference held at Sevilla University in the summer of 2011. The topics include spectral theory, differential operators, integral operators, composition operators, Toeplitz operators, and more. The book also presents a large number of techniques in operator theory.
Download or read book Second Summer School in Analysis and Mathematical Physics written by Salvador Pérez-Esteva and published by American Mathematical Soc.. This book was released on 2001 with total page 288 pages. Available in PDF, EPUB and Kindle. Book excerpt: For the second time, a Summer School in Analysis and Mathematical Physics took place at the Universidad Nacional Autonoma de Mexico in Cuernavaca. The purpose of the schools is to provide a bridge from standard graduate courses in mathematics to current research topics, particularly in analysis. The lectures are given by internationally recognized specialists in the fields. The topics covered in this Second Summer School include harmonic analysis, complex analysis, pseudodifferential operators, the mathematics of quantum chaos, and non-linear analysis.
Download or read book On Necessary and Sufficient Conditions for L p Estimates of Riesz Transforms Associated to Elliptic Operators on mathbb R n and Related Estimates written by Pascal Auscher and published by American Mathematical Soc.. This book was released on 2007 with total page 102 pages. Available in PDF, EPUB and Kindle. Book excerpt: This memoir focuses on $Lp$ estimates for objects associated to elliptic operators in divergence form: its semigroup, the gradient of the semigroup, functional calculus, square functions and Riesz transforms. The author introduces four critical numbers associated to the semigroup and its gradient that completely rule the ranges of exponents for the $Lp$ estimates. It appears that the case $p2$ which is new. The author thus recovers in a unified and coherent way many $Lp$ estimates and gives further applications. The key tools from harmonic analysis are two criteria for $Lp$ boundedness, one for $p2$ but in ranges different from the usual intervals $(1,2)$ and $(2,\infty)$.
