Carleman estimates for parabolic equations with super strong degeneracy in a set of positive measure

TL;DR

This paper develops new Carleman estimates for linear parabolic equations with super strong degeneracy in a positive measure set, leading to null controllability results when the control domain includes the degeneracy set.

Contribution

It introduces novel Carleman estimates for highly degenerate parabolic equations and establishes null controllability under these challenging conditions.

Findings

New Carleman estimates for super strongly degenerate parabolic equations.

Null controllability achieved when control domain contains degeneracy set.

Applicable to equations with degeneracy on positive measure subsets.

Abstract

This work is concerned with the obtainment of new Carleman estimates for linear parabolic equations, where the second-order differential operator brings a super strong degeneracy in a positive measure subset of the spatial domain. In order to prove our main result, the control domain is supposed to contain the set of degeneracies. As a well-known consequence, we achieve a null controllability result in the current context.