On the isoperimetric inequality for the magnetic Robin Laplacian with negative boundary parameter

TL;DR

This paper investigates the magnetic Robin Laplacian with negative boundary parameters, demonstrating that the disk maximizes ground state energy among certain domains under fixed perimeter and moderate magnetic field strength.

Contribution

It proves a new isoperimetric inequality for the magnetic Robin Laplacian, identifying the disk as the maximizer within a broad class of domains.

Findings

The disk maximizes the ground state energy among certain domains.

The result holds under fixed perimeter and moderate magnetic field strength.

Includes all convex centrally symmetric domains.

Abstract

We consider the magnetic Robin Laplacian with a negative boundary parameter. Among a certain class of domains, we prove that the disk maximizes 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 convex centrally symmetric domains.