Unique continuation and classification of blow-up profiles for elliptic systems with Neumann boundary coupling and applications to higher order fractional equations

TL;DR

This paper develops a monotonicity formula for elliptic systems with Neumann boundary coupling, enabling the classification of blow-up profiles and establishing strong unique continuation for certain higher order fractional equations.

Contribution

It introduces a new monotonicity formula for elliptic systems with boundary coupling, advancing the understanding of blow-up behavior and unique continuation in higher order fractional PDEs.

Findings

Established a monotonicity formula for elliptic systems with Neumann boundary coupling.

Proved strong unique continuation for specific fourth order and fractional equations.

Classified blow-up profiles for the studied elliptic systems.

Abstract

In this paper we develop a monotonicity formula for elliptic systems with Neumann boundary coupling, proving unique continuation and classification of blow-up profiles. As an application, we obtain strong unique continuation for some fourth order equations and higher order fractional problems.