An elliptic adaptation of ideas of Carleman and Domar from complex analysis related to Levinson's log log theorem

TL;DR

This paper extends classical complex analysis theorems to linear elliptic PDEs using the three balls inequality, providing a new perspective on Levinson's loglog theorem.

Contribution

It adapts Carleman and Domar's ideas from complex analysis to elliptic PDEs, generalizing Levinson's loglog theorem.

Findings

Generalization of Levinson's loglog theorem to elliptic PDEs

Application of three balls inequality in the adaptation

New insights into elliptic PDE behavior

Abstract

Using the three balls inequality, we adapt the elegant ideas of Carleman and Domar from complex analysis to linear elliptic PDE and generalize the classical Levinson's loglog theorem.