Controllability of strongly degenerate parabolic problems with strongly singular potentials

Abstract

We prove a null controllability result for a parabolic Dirichlet problem with non smooth coefficients in presence of strongly singular potentials and a coefficient degenerating at an interior point. We cover the case of weights falling out the class of Muckenhoupt functions, so that no Hardy-type inequality is available; for instance, we can consider Coulomb-type potentials. However, through a cut-off function method, we recover the desired controllability result.

Keywords

• strong degeneracy
• strong singularity
• non smooth coefficients
• coulomb potential
• null controllability
• cut-off functions