# Unique continuation principles in cones under nonzero Neumann boundary conditions

## TL;DR

This paper establishes unique continuation principles for elliptic equations in conical domains with Neumann boundary conditions, accommodating singularities and providing classification of blow-up limits.

## Contribution

It introduces novel unique continuation results for elliptic equations in cones with nonzero Neumann conditions, even with singularities at the vertex.

## Key findings

- Unique continuation results for elliptic equations in cones
- Classification of blow-up limits in this setting
- Use of Almgren-type frequency formula with remainders

## Abstract

We consider an elliptic equation in a cone, endowed with (possibly inhomogeneous) Neumann conditions. The operator and the forcing terms can also allow non-Lipschitz singularities at the vertex of the cone. In this setting, we provide unique continuation results, both in terms of interior and boundary points. The proof relies on a suitable Almgren-type frequency formula with remainders. As a byproduct, we obtain classification results for blow-up limits.