Singular Integral Operators, Quantitative Flatness, and Boundary Problems

Juan José Marín, José María Martell, Dorina Mitrea, Irina Mitrea, Marius Mitrea (Autoren)

Buch | Hardcover

VIII, 601 Seiten

2022 | 1st ed. 2022
Springer International Publishing (Verlag)
978-3-031-08233-7 (ISBN)

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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.

Juan Jose Marin is a harmonic analyst whose research interests also include boundary value problems and geometric measure theory. He received a Ph.D. in mathematics in 2019 from Universidad Aut/'onoma de Madrid and Instituto de Ciencias Matem/'aticas, Spain, working under the supervision of Jose Maria Martell and Marius Mitrea. Jose Maria Martell is a mathematician specializing in the areas of harmonic analysis, partial differential equations, and geometric measure theory. He received a Ph.D. in mathematics from Universidad Autonoma de Madrid, Spain, working under the supervision of Jose Garcia-Cuerva. Jose Maria Martell is currently serving as the director of Instituto de Matematicas, Spain. Dorina Mitrea is a mathematician specializing in the areas of harmonic analysis, partial differential equations, geometric measure theory, and global analysis. She received a Ph.D. in mathematics from the University of Minnesota, working under the supervision of Eugene Fabes. Dorina Mitrea is currently serving as the chair of the Department of Mathematics, Baylor University, USA. Irina Mitrea is an L.H. Carnell Professor and chair of the Department of Mathematics at Temple University whose expertise lies at the interface between the areas of harmonic analysis, partial differential equations, and geometric measure theory. She received her Ph.D. in mathematics from the University of Minnesota, working under the supervision of Carlos Kenig and Mikhail Safanov. Irina Mitrea is a Fellow of the American Mathematical Society and a Fellow of the Association for Women in Mathematics. She received a Simons Foundation Fellowship, a Von Neumann Fellowship at the Institute for Advanced Study, Princeton, and is a recipient of the Ruth Michler Memorial Prize from the Association for Women in Mathematics. Marius Mitrea is a mathematician whose research interests lay at the confluence between harmonic analysis, partial differential equations, geometric measure theory, global analysis, and scattering. He received a Ph.D. in mathematics from the University of South Carolina, USA, working under the supervision of Bjoern D. Jawerth. Marius Mitrea is a Fellow of the American Mathematical Society.

Introduction.- Geometric Measure Theory.- Calderon-Zygmund Theory for Boundary Layers in UR Domains.- Boundedness and Invertibility of Layer Potential Operators.- Controlling the BMO Semi-Norm of the Unit Normal.- Boundary Value Problems in Muckenhoupt Weighted Spaces.- Singular Integrals and Boundary Problems in Morrey and Block Spaces.- Singular Integrals and Boundary Problems in Weighted Banach Function Spaces.

Erscheinungsdatum	01.10.2022
Reihe/Serie	Progress in Mathematics
Zusatzinfo	VIII, 601 p. 5 illus., 3 illus. in color.
Verlagsort	Cham
Sprache	englisch
Maße	155 x 235 mm
Gewicht	1075 g
Themenwelt	Mathematik / Informatik ► Mathematik ► Analysis
Themenwelt	Mathematik / Informatik ► Mathematik ► Wahrscheinlichkeit / Kombinatorik
Schlagworte	Ahlfors regular domain • Block space • Boundary layer potential • Boundary value problem • geometric measure theory • Morrey space • Muckenhoupt weight • Muckenhoupt weighted Sobolev space • Nontangentially accessible domain • singular integral operators • Uniformly rectifiable domain
ISBN-10	3-031-08233-8 / 3031082338
ISBN-13	978-3-031-08233-7 / 9783031082337
Zustand	Neuware