Moritz Egert – författare
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5 produkter
5 produkter
Del 346 - Progress in Mathematics
Boundary Value Problems and Hardy Spaces for Elliptic Systems with Block Structure
Inbunden, Engelska, 2023
1 418 kr
Skickas inom 10-15 vardagar
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.
E-bok
Engelska, 20231 741 kr
Läs direkt efter köp
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.
625 kr
Skickas inom 5-8 vardagar
Del 346 - Progress in Mathematics
Boundary Value Problems and Hardy Spaces for Elliptic Systems with Block Structure
Häftad, Engelska, 2024
1 418 kr
Skickas inom 10-15 vardagar
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.
Inbunden, Engelska, 2026
774 kr
Kommande
The study of the Laplacian through the Fourier transform lies at the center of classical harmonic analysis. It is Plancherel’s theorem that intimately links square-integrable functions with the theory of weak derivatives and a symbolic calculus for the Laplacian. Examples include Littlewood–Paley inequalities, Riesz transform estimates and Calderón–Zygmund extrapolation. Over the last decades, the quest to generalize these properties to elliptic operators L in divergence form with bounded measurable coefficients has triggered the development of new techniques that led to a surge of spectacular results in elliptic and parabolic PDE theory.Assuming only undergraduate knowledge in analysis and some background on Hilbert spaces and the Fourier transform, the authors develop the cornerstones of this ‘L-adapted Fourier analysis’ over 14 consecutive lectures. As they delve deeper into the topic, readers make first encounters with maximal functions, Carleson measures and a T(b) theorem. The lectures culminate in a self-contained presentation of the solution to the Kato conjecture, a challenging problem that resisted solution for 40 years until it was finally solved in 2001.This book can serve as a fully developed curriculum for a first graduate course in harmonic analysis and PDEs. Based on the 27th Internet Seminar on Evolution Equations, organized by the authors in the 2023/24 academic year, each lecture is enriched with original exercises, detailed solutions, and video presentations guiding through each theorem’s proof and offering additional insights.