David G., Feneuil J., Mayboroda S. Elliptic theory in domains with boundaries of mixed dimension

Paris: Société Mathématique de France, 2023. — 152 p.Motivation and a general overview of the main results
Motivation
Additional historical comments
A rough outline of the main assumptions and results
Our assumptions
Some examples where our assumptions hold
Classical elliptic operators
Ahlfors regular sets
Caffarelli and Sylvestre fractional operators
Sawtooth domains
Balls minus an Ahlfors regular set of low dimension
Nearly t-independent A2-weights
Stranger measures
The definition of the space W
The access cones and their properties
The Trace Theorem
Poincaré inequalities on the boundary
The Extension Theorem
Completeness of W and density of smooth functions
The localized versions Wr(E) of our energy space W
Definitions of solutions and their properties
Construction of the harmonic measure
Bounded boundaries
Green functions
Comparison principle
Bibliography