Elliptic Boundary Value Problems with Fractional Regularity Data : The First Order Approach (Crm Monograph Series)

Amenta, Alex/ Auscher, Pascal

American Mathematical Society（2018/05発売）

• 製本 Hardcover:ハードカバー版／ページ数 152 p.
• 言語 ENG
• 商品コード 9781470442507
• DDC分類 515.35

Full Description

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.

Contents

Introduction
Function space preliminaries
Operator theoretic preliminaries
Adapted Besov-Hardy-Sobolev spaces
Spaces adapted to perturbed Dirac operators
Classification of solutions to Cauchy-Riemann systems and elliptic equations
Applications to boundary value problems
Bibliography
Index.