Optimal energy growth lower bounds for a class of solutions to the vectorial Allen-Cahn equation

Abstract

We prove optimal lower bounds for the growth of the energy over balls of minimizers to the vectorial Allen-Cahn energy in two spatial dimensions, as the radius tends to infinity. In the case of radially symmetric solutions, we can prove a stronger result in all dimensions.

Cited by in corpus (4)

• Energy estimates for minimizers to a class of elliptic systems of Allen-Cahn type and the Liouville property
• On a maximum principle for vector minimizers to the Allen-Cahn energy
• A Liouville type result for bounded, entire solutions to a class of variational semilinear elliptic systems
• A Liouville theorem for minimizers with finite potential energy for the vectorial Allen-Cahn equation