Elliptic Boundary Value Problems With Fractional Regularity Data The First Order Approach

Author : Alex Amenta
Publisher : American Mathematical Soc.
ISBN 13 : 1470442507
Total Pages : 152 pages
Book Rating : 4.07/5 ( download)

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Download or read book Elliptic Boundary Value Problems with Fractional Regularity Data: The First Order Approach written by Alex Amenta and published by American Mathematical Soc.. This book was released on 2018-04-03 with total page 152 pages. Available in PDF, EPUB and Kindle. Book excerpt: A co-publication of the AMS and Centre de Recherches Mathématiques In this monograph the authors study the well-posedness of boundary value problems of Dirichlet and Neumann type for elliptic systems on the upper half-space with coefficients independent of the transversal variable and with boundary data in fractional Hardy–Sobolev and Besov spaces. The authors use the so-called “first order approach” which uses minimal assumptions on the coefficients and thus allows for complex coefficients and for systems of equations. This self-contained exposition of the first order approach offers new results with detailed proofs in a clear and accessible way and will become a valuable reference for graduate students and researchers working in partial differential equations and harmonic analysis.

Author : Pascal Auscher
Publisher : Springer Nature
ISBN 13 : 3031299736
Total Pages : 310 pages
Book Rating : 4.35/5 ( download)

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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.

Author : Tuomas Hytönen
Publisher : Springer
ISBN 13 : 3319698087
Total Pages : 616 pages
Book Rating : 4.83/5 ( download)

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Download or read book Analysis in Banach Spaces written by Tuomas Hytönen and published by Springer. This book was released on 2018-02-14 with total page 616 pages. Available in PDF, EPUB and Kindle. Book excerpt: This second volume of Analysis in Banach Spaces, Probabilistic Methods and Operator Theory, is the successor to Volume I, Martingales and Littlewood-Paley Theory. It presents a thorough study of the fundamental randomisation techniques and the operator-theoretic aspects of the theory. The first two chapters address the relevant classical background from the theory of Banach spaces, including notions like type, cotype, K-convexity and contraction principles. In turn, the next two chapters provide a detailed treatment of the theory of R-boundedness and Banach space valued square functions developed over the last 20 years. In the last chapter, this content is applied to develop the holomorphic functional calculus of sectorial and bi-sectorial operators in Banach spaces. Given its breadth of coverage, this book will be an invaluable reference to graduate students and researchers interested in functional analysis, harmonic analysis, spectral theory, stochastic analysis, and the operator-theoretic approach to deterministic and stochastic evolution equations.

Author : Ivo Babuška
Publisher :
ISBN 13 :
Total Pages : 140 pages
Book Rating : 4.62/5 ( download)

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Download or read book Regularity of the Solution of Elliptic Problems with Piecewise Analytic Data written by Ivo Babuška and published by . This book was released on 1986 with total page 140 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Author : Luis Angel Caffarelli
Publisher : Edizioni della Normale
ISBN 13 : 9788876422492
Total Pages : 0 pages
Book Rating : 4.98/5 ( download)

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Download or read book The obstacle problem written by Luis Angel Caffarelli and published by Edizioni della Normale. This book was released on 1999-10-01 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: The material presented here corresponds to Fermi lectures that I was invited to deliver at the Scuola Normale di Pisa in the spring of 1998. The obstacle problem consists in studying the properties of minimizers of the Dirichlet integral in a domain D of Rn, among all those configurations u with prescribed boundary values and costrained to remain in D above a prescribed obstacle F. In the Hilbert space H1(D) of all those functions with square integrable gradient, we consider the closed convex set K of functions u with fixed boundary value and which are greater than F in D. There is a unique point in K minimizing the Dirichlet integral. That is called the solution to the obstacle problem.

Author : Pavel B. Bochev
Publisher : Springer Science & Business Media
ISBN 13 : 0387689222
Total Pages : 669 pages
Book Rating : 4.27/5 ( download)

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Download or read book Least-Squares Finite Element Methods written by Pavel B. Bochev and published by Springer Science & Business Media. This book was released on 2009-04-28 with total page 669 pages. Available in PDF, EPUB and Kindle. Book excerpt: Since their emergence, finite element methods have taken a place as one of the most versatile and powerful methodologies for the approximate numerical solution of Partial Differential Equations. These methods are used in incompressible fluid flow, heat, transfer, and other problems. This book provides researchers and practitioners with a concise guide to the theory and practice of least-square finite element methods, their strengths and weaknesses, established successes, and open problems.

Author : Stephan Dahlke
Publisher :
ISBN 13 :
Total Pages : 16 pages
Book Rating : 4.30/5 ( download)

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Download or read book Besov regularity for elliptic boundary value problems written by Stephan Dahlke and published by . This book was released on 1995 with total page 16 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Author : Serge Levendorskii
Publisher : Springer Science & Business Media
ISBN 13 : 9401712158
Total Pages : 442 pages
Book Rating : 4.56/5 ( download)

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Download or read book Degenerate Elliptic Equations written by Serge Levendorskii and published by Springer Science & Business Media. This book was released on 2013-11-11 with total page 442 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume is the first to be devoted to the study of various properties of wide classes of degenerate elliptic operators of arbitrary order and pseudo-differential operators with multiple characteristics. Conditions for operators to be Fredholm in appropriate weighted Sobolev spaces are given, a priori estimates of solutions are derived, inequalities of the Grding type are proved, and the principal term of the spectral asymptotics for self-adjoint operators is computed. A generalization of the classical Weyl formula is proposed. Some results are new, even for operators of the second order. In addition, an analogue of the Boutet de Monvel calculus is developed and the index is computed. For postgraduate and research mathematicians, physicists and engineers whose work involves the solution of partial differential equations.

Author :
Publisher :
ISBN 13 :
Total Pages : 1026 pages
Book Rating : 4.49/5 ( download)

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Download or read book Scientific and Technical Aerospace Reports written by and published by . This book was released on with total page 1026 pages. Available in PDF, EPUB and Kindle. Book excerpt: Lists citations with abstracts for aerospace related reports obtained from world wide sources and announces documents that have recently been entered into the NASA Scientific and Technical Information Database.

Author : Isaac Pesenson
Publisher : Birkhäuser
ISBN 13 : 3319555561
Total Pages : 510 pages
Book Rating : 4.60/5 ( download)

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Download or read book Recent Applications of Harmonic Analysis to Function Spaces, Differential Equations, and Data Science written by Isaac Pesenson and published by Birkhäuser. This book was released on 2017-08-09 with total page 510 pages. Available in PDF, EPUB and Kindle. Book excerpt: The second of a two volume set on novel methods in harmonic analysis, this book draws on a number of original research and survey papers from well-known specialists detailing the latest innovations and recently discovered links between various fields. Along with many deep theoretical results, these volumes contain numerous applications to problems in signal processing, medical imaging, geodesy, statistics, and data science. The chapters within cover an impressive range of ideas from both traditional and modern harmonic analysis, such as: the Fourier transform, Shannon sampling, frames, wavelets, functions on Euclidean spaces, analysis on function spaces of Riemannian and sub-Riemannian manifolds, Fourier analysis on manifolds and Lie groups, analysis on combinatorial graphs, sheaves, co-sheaves, and persistent homologies on topological spaces. Volume II is organized around the theme of recent applications of harmonic analysis to function spaces, differential equations, and data science, covering topics such as: The classical Fourier transform, the non-linear Fourier transform (FBI transform), cardinal sampling series and translation invariant linear systems. Recent results concerning harmonic analysis on non-Euclidean spaces such as graphs and partially ordered sets. Applications of harmonic analysis to data science and statistics Boundary-value problems for PDE's including the Runge–Walsh theorem for the oblique derivative problem of physical geodesy.