Boundary Harnack Principle on Nodal Domains
Fanghua Lin, Zhengjiang Lin
TL;DR
This paper investigates geometric and potential theoretic properties of nodal domains of solutions to elliptic equations, establishing key boundary estimates and inequalities.
Contribution
It introduces boundary Harnack inequalities and corkscrew conditions for nodal domains of elliptic solutions, advancing understanding of their geometric structure.
Findings
Established corkscrew conditions for nodal domains
Proved Carleson type estimates on these domains
Derived boundary Harnack inequalities
Abstract
We study some geometric and potential theoretic properties of nodal domains of solutions to certain uniformly elliptic equations. In particular, we establish corkscrew conditions, Carleson type estimates and boundary Harnack inequalities on a class of nodal domains.
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Taxonomy
TopicsAdvanced Harmonic Analysis Research · Nonlinear Partial Differential Equations · Differential Equations and Boundary Problems