Singular Integral Operators, Quantitative Flatness, and Boundary Problems

Beschreibung

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.
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.

Presents many significant new results on the topic of singular integral operators and boundary value problems Contributes to ongoing efforts to establish a bridge between analysis and geometry Includes many complete proofs appearing in publication for the first time

Autor*in

Juan José Marín

Themen in »Singular Integral Operators, Quantitative Flatness, and Boundary Problems«

Geometric Measure Theory Singular integral operators Boundary value problem Boundary layer potential Ahlfors regular domain Uniformly rectifiable domain Nontangentially accessible domain Muckenhoupt weight Muckenhoupt weighted Sobolev space Morrey space Block space

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“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)

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