Singular Integral Operators, Quantitative Flatness, and Boundary Problems
Juan José Marín, José María Martell, Dorina Mitrea, Irina Mitrea, Marius Mitrea, 3031082338, 978-3031082337, 9783031082337, 978-3-031-08233-7, 978-3-031-08234-4
This 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.