Boundary Value Problems And Hardy Spaces For Elliptic Systems With Block Structure
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Boundary Value Problems And Hardy Spaces For Elliptic Systems With Block Structure
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Author : Pascal Auscher
language : en
Publisher: Springer Nature
Release Date : 2023-07-27
Boundary Value Problems And Hardy Spaces For Elliptic Systems With Block Structure written by Pascal Auscher and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-07-27 with Mathematics categories.
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.
Square Roots Of Elliptic Systems In Locally Uniform Domains
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Author : Sebastian Bechtel
language : en
Publisher: Springer Nature
Release Date : 2024-09-09
Square Roots Of Elliptic Systems In Locally Uniform Domains written by Sebastian Bechtel and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-09-09 with Mathematics categories.
This book establishes a comprehensive theory to treat square roots of elliptic systems incorporating mixed boundary conditions under minimal geometric assumptions. To lay the groundwork, the text begins by introducing the geometry of locally uniform domains and establishes theory for function spaces on locally uniform domains, including interpolation theory and extension operators. In these introductory parts, fundamental knowledge on function spaces, interpolation theory and geometric measure theory and fractional dimensions are recalled, making the main content of the book easier to comprehend. The centerpiece of the book is the solution to Kato's square root problem on locally uniform domains. The Kato result is complemented by corresponding Lp bounds in natural intervals of integrability parameters. This book will be useful to researchers in harmonic analysis, functional analysis and related areas.
Integro Differential Elliptic Equations
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Author : Xavier Fernández-Real
language : en
Publisher: Springer Nature
Release Date : 2024-04-24
Integro Differential Elliptic Equations written by Xavier Fernández-Real and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-04-24 with Mathematics categories.
This monograph offers a self-contained introduction to the regularity theory for integro-differential elliptic equations, mostly developed in the 21st century. This class of equations finds relevance in fields such as analysis, probability theory, mathematical physics, and in several contexts in the applied sciences. The work gives a detailed presentation of all the necessary techniques, with a primary focus on the main ideas rather than on proving all the results in their greatest generality. The basic building blocks are presented first, with the study of the square root of the Laplacian, and weak solutions to linear equations. Subsequently, the theory of viscosity solutions to nonlinear equations is developed, and proofs are provided for the main known results in this context. The analysis finishes with the investigation of obstacle problems for integro-differential operators and establishes the regularity of solutions and free boundaries. A distinctive feature of this work lies in its presentation of nearly all covered material in a monographic format for the first time, and several proofs streamline, and often simplify, those in the original papers. Furthermore, various open problems are listed throughout the chapters.
Suprematism In Harmonic Analysis
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Author : Antonio Córdoba
language : en
Publisher: Springer Nature
Release Date : 2024-11-08
Suprematism In Harmonic Analysis written by Antonio Córdoba and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-11-08 with Mathematics categories.
This award-winning monograph explores advanced topics in harmonic analysis, addressing both classical and contemporary problems. Several connections to number theory, crystallography or atomic theory are also surveyed. The term “suprematism” refers to a certain geometric point of view underlying proofs and arguments. The opening of the book is dedicated to a few results, with short statements and proofs, that could be called “mathematical haikus”. Then, in the first part of the book, singular integrals beyond the classical Calderón-Zygmund theory, such as Vitali-type covering lemmas and estimates for the corresponding maximal operators, are explored. The exponential overlapping of parallelepipeds, the strong maximal function, and Zygmund's conjecture about monotonic bases are also covered. The core of this part is devoted to the Kakeya maximal function and its relation to the spherical summation of Fourier series and integrals. The two-dimensional case is well understood, but the case of higher dimensions still presents many open problems and conjectures. The chapters in the second part of the book treat questions at the interface of harmonic analysis and number theory, including applications of the Poisson summation formula to crystallography and arithmetic, estimates of the Minkowski dimension of Riemann graphs, random lattice point problems, and the role of Weyl sums in atomic energy oscillations. With a focus on rigorous research insights for graduate students and researchers in mathematics, this book provides a comprehensive journey through the hidden landscapes of harmonic analysis.
S Ntesi Mem Ria 2021 2022
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Author : Institut d'Estudis Catalans
language : ca
Publisher: Institut d'Estudis Catalans
Release Date : 2022-11-01
S Ntesi Mem Ria 2021 2022 written by Institut d'Estudis Catalans and has been published by Institut d'Estudis Catalans this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-11-01 with Education categories.
Mathematical Reviews
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Author :
language : en
Publisher:
Release Date : 2003
Mathematical Reviews written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2003 with Mathematics categories.
Bernoulli Free Boundary Problems
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Author : Eugene Shargorodsky
language : en
Publisher: American Mathematical Soc.
Release Date : 2008
Bernoulli Free Boundary Problems written by Eugene Shargorodsky and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008 with Mathematics categories.
Questions of existence, multiplicity, and regularity of free boundaries for prescribed data need to be addressed and their solutions lead to nonlinear problems. In this paper an equivalence is established between Bernoulli free-boundary problems and a class of equations for real-valued functions of one real variable.
Physics Briefs
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Author :
language : en
Publisher:
Release Date : 1990
Physics Briefs written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1990 with Physics categories.
Encyclopaedia Of Mathematics
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Author : Michiel Hazewinkel
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Encyclopaedia Of Mathematics written by Michiel Hazewinkel and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.
This is the second supplementary volume to Kluwer's highly acclaimed eleven-volume Encyclopaedia of Mathematics. This additional volume contains nearly 500 new entries written by experts and covers developments and topics not included in the previous volumes. These entries are arranged alphabetically throughout and a detailed index is included. This supplementary volume enhances the existing eleven volumes, and together these twelve volumes represent the most authoritative, comprehensive and up-to-date Encyclopaedia of Mathematics available.
An Index And Other Useful Information 501 1000
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Author : Albrecht Dold
language : en
Publisher:
Release Date : 1984
An Index And Other Useful Information 501 1000 written by Albrecht Dold and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1984 with Lecture notes in mathematics (Springer-Verlag) categories.