Boundary value problems and hardy spaces for elliptic systems with block structure / Pascal Auscher, Moritz Egert.

Format:

Book

Author/Creator:

Auscher, Pascal, Author.

Series:

Progress in mathematics (Boston, Mass.) ; v. 346.

Progress in mathematics, 0743-1643 ; volume 346

Language:

English

Subjects (All):

Differential equations, Elliptic.

Boundary value problems.

Hardy spaces.

Physical Description:

xiii, 310 pages : some illustrations ; 25 cm

Place of Publication:

Cham, Switzerland : Birkhäuser, [2023]

Summary:

"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.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."-- Provided by publisher.

Notes:

Includes bibliographical references (pages 301-305) and index.

Other Format:

e-book version

ISBN:

9783031299728

3031299728

OCLC:

1394346947

Publisher Number:

9783031299728