We continue our exploration of geometrical objects on the Grushin plane with some of their applications. It turns out that stable solutions of the Allen-Cahn equation in the Grushin plane satisfy a Sobolev-Poincare inequality. Such inequality bounds the weighted L²-norm of a test function by a weighted L²-norm of its gradient, and the weights involve geometry-related quantities.
Meeting ID: 864 6625 4294 Passcode: 992805