Nonsmooth Boundary Value Problems

Explore the intricacies of nonsmooth boundary value problems in this 46-minute AMS-AWM Noether Lecture given by Jill Pipher from Brown University at the 2018 Joint Mathematics Meetings. Delve into complex function theory, dual problems, and bounded mean oscillation. Examine the self-improving properties of Hilbert transforms and bounded operators. Investigate BMO functions, LP spaces, and regularity in the context of nonsmooth coefficients. Analyze Helder continuity, weak solutions, and properties of harmonic functions. Study the Durst problem, boundary value problems, and the Kanto conjecture. Explore the nonself-adjoint case, Carlos measure characterization, and BMO solvability. Consider boundary geometry and open problems in bounded domains, gaining insights into this advanced mathematical topic.

Introduction
Outline
Complex Function Theory
Dual Problem
Bounded Mean Oscillation
Bounded Oscillation
Self Improving Properties
Hilbert Transform
Bounded Operators
BMO Functions
LP Spaces
regularity
divergence
nonsmooth coefficients
Helder continuity
Weak solution
Pfefferman
Properties of Harmonic Functions
Durst a Problem
Boundary Value Problems
Examples
Kanto conjecture
Nonself adjoint case
Carlos measure characterization
BMOsolvability
Boundary Geometry
Open Problems
Bounded Domains