"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"--
Many geometric and analytic properties of sets hinge on the properties of elliptic measures, notoriously missing for sets of higher co-dimensions. Here, David, Feneuil, and Mayboroda develop a version of elliptic theory, associated to a linear partial differential equation, that ultimately yields a notion analogous to that of the harmonic measures, for sets of codimension higher than one. Among their topics are the Harnack chain condition and the doubling property, completeness and density of smooth functions, the chain rule and applications, definition of solutions, and the comparison principle. Annotation ©2022 Ringgold, Inc., Portland, OR (protoview.com)
