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.
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Alex Amenta, Delft University of Technology, The Netherlands.
Pascal Auscher, Universite Paris-Sud, Orsay, France.
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
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