eBook

Elliptic Theory for Sets with Higher Co-dimensional Boundaries

David, G., Feneuil, J., Mayboroda, S.

2022

Overview

Many geometric and analytic properties of sets hinge on the properties of elliptic measure, notoriously missing for sets of higher co-dimension. The aim of this manuscript is to develop a version of elliptic theory, associated to a linear PDE, which ultimately yields a notion analogous to that of the harmonic measure, for sets of codimension higher than 1. To this end, we turn to degenerate elliptic equations. Let In another article to appear, we will prove that when

• Publisher: American Mathematical Society
• Subject: Boundary value problems / Degenerate differential equations / Differential equations, Elliptic / Harmonic analysis / Harmonic analysis on Euclidean spaces -- Harmonic analysis in several variables -- Harmonic analysis and PDE. msc / Harmonic analysis on Euclidean spaces -- Harmonic analysis in several variables -- Maximal functions, Littlewood-Paley theory. msc / Harmonic analysis on Euclidean spaces -- Harmonic analysis in several variables -- Singular and oscillatory integrals (Calderón-Zygmund, etc.). msc / Harmonic functions / Measure and integration -- Classical measure theory -- Hausdorff and packing measures. msc / Measure and integration -- Classical measure theory -- Length, area, volume, other geometric measure theory. msc / Partial differential equations -- Elliptic equations and systems -- Boundary value problems for second-order elliptic equations. msc / Partial differential equations -- Elliptic equations and systems -- Degenerate elliptic equations. msc / Potential theory -- Higher-dimensional theory -- Harmonic, subharmonic, superharmonic functions. msc
• ISBN: 9781470450434, 1470450437