“The book is very well written and should become a standard reference for further research in this area. It joins a massive collection of excellent books by the authors and their collaborators.” (Mario Milman, Mathematical Reviews, August, 2024)
Singular Integral Operators, Quantitative Flatness, and Boundary Problems
von Juan José Marín, José María Martell, Dorina Mitrea, Irina Mitrea und Marius MitreaThis monograph provides a state-of-the-art, self-contained account on the effectiveness of the method of boundary layer potentials in the study of elliptic boundary value problems with boundary data in a multitude of function spaces. Many significant new results are explored in detail, with complete proofs, emphasizing and elaborating on the link between the geometric measure-theoretic features of an underlying surface and the functional analytic properties of singular integral operators defined on it. Graduate students, researchers, and professionals interested in a modern account of the topic of singular integral operators and boundary value problems – as well as those more generally interested in harmonic analysis, PDEs, and geometric analysis – will find this text to be a valuable addition to the mathematical literature.
