An optimal spectral inequality for degenerate operators

TL;DR

This paper proves a spectral inequality for a degenerate elliptic operator using Carleman and moment methods, enabling null controllability results for the degenerate heat equation on measurable sets.

Contribution

It introduces an optimal spectral inequality for degenerate operators, combining Carleman techniques with the moment method, advancing control theory for degenerate PDEs.

Findings

Established a Lebeau-Robbiano spectral inequality for degenerate elliptic operators.

Demonstrated null controllability on measurable sets in time for the degenerate heat equation.

Combined Carleman and moment methods to achieve the main results.

Abstract

In this paper we establish a Lebeau-Robbiano spectral inequality for a degenerate one dimensional elliptic operator. Carleman techniques and moment method are combined. Application to null controllability on a measurable set in time for the degenerated heat equation is described.