Singular Integral Operators, Quantitative Flatness, and Boundary Problems

Juan Jose Marin,Jose Maria Martell,Dorina Mitrea,Irina Mitrea,Marius Mitrea

Birkhauser Verlag AG
24 October 2022

Singular Integral Operators, Quantitative Flatness, and Boundary Problems

Juan Jose Marin,Jose Maria Martell,Dorina Mitrea,Irina Mitrea,Marius Mitrea

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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.

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