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.
- Publication:
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arXiv e-prints
- Pub Date:
- February 2014
- DOI:
- arXiv:
- arXiv:1402.3844
- Bibcode:
- 2014arXiv1402.3844S
- Keywords:
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- Mathematics - Analysis of PDEs