Boundary value problems and hardy spaces for elliptic systems with block structure
Auscher, Pascal
Boundary value problems and hardy spaces for elliptic systems with block structure [Documento eletrónico] / Pascal Auscher, Moritz Egert. - Cham : Springer International Publishing : Birkhäuser , 2023 . - XIII, 310 p. : il.. - (Progress in Mathematics) ; vol. 346 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.
Clicar aqui para aceder a um recurso externo
ISBN 978-3-031-29973-5
Differential equations
Harmonic analysis
Operator theory
Functional analysis
LCC QA370-380
Boundary value problems and hardy spaces for elliptic systems with block structure [Documento eletrónico] / Pascal Auscher, Moritz Egert. - Cham : Springer International Publishing : Birkhäuser , 2023 . - XIII, 310 p. : il.. - (Progress in Mathematics) ; vol. 346 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.
Clicar aqui para aceder a um recurso externo
ISBN 978-3-031-29973-5
Differential equations
Harmonic analysis
Operator theory
Functional analysis
LCC QA370-380
