Geometric Harmonic Analysis V Fredholm Theory And Finer Estimates For Integral Operators With Applications To Boundary Problems 1st Edition Dorina Mitrea by Dorina Mitrea, Irina Mitrea, Marius Mitrea 9783031315602, 9783031315619, 303131560X, 3031315618 instant download after payment.

Mathematics Subject Classification: 32A Holomorphic functions of several complex variables • 26B20 Integral formulas of real functions of several variables (Stokes, Gauss, Green, etc.) • 31B Higher-dimensional potential theory • 35J Elliptic equations and elliptic systems • 42B Harmonic analysis in several variables

This monograph presents a comprehensive, self-contained, and novel approach to the Divergence Theorem through five progressive volumes. Its ultimate aim is to develop tools in Real and Harmonic Analysis, of geometric measure theoretic flavor, capable of treating a broad spectrum of boundary value problems formulated in rather general geometric and analytic settings. The text is intended for researchers, graduate students, and industry professionals interested in applications of harmonic analysis and geometric measure theory to complex analysis, scattering, and partial differential equations.

The ultimate goal in Volume V is to prove well-posedness and Fredholm solvability results concerning boundary value problems for elliptic second-order homogeneous constant (complex) coefficient systems, and domains of a rather general geometric nature. The formulation of the boundary value problems treated here is optimal from a multitude of points of view, having to do with geometry, functional analysis (through the consideration of a large variety of scales of function spaces), topology, and partial differential equations.