On the Isoperimetric Inequality for the Magnetic Robin Laplacian with Negative Boundary Parameter

Abstract

We consider the magnetic Robin Laplacian with a negative boundary parameter on a bounded, planar C2-smooth domain. The respective magnetic field is homogeneous. Among a certain class of domains, we prove that the disk maximises the ground-state energy under the fixed perimeter constraint provided that the magnetic field is of moderate strength. This class of domains includes, in particular, all domains that are contained upon translations in the disk of the same perimeter and all centrally symmetric domains. © 2022, Mathematica Josephina, Inc.