Amenta A., Auscher P. Elliptic Boundary Value Problems with Fractional Regularity Data: The First Order Approach

American Mathematical Society, 2018. — 161 p. — (CRM Monograph Series 37). — ISBN: 1470442507.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.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