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Optimal potential energy growth lower bounds for minimizing solutions to the vectorial Allen–Cahn equation in two space dimensions
Author(s) -
Sourdis Christos
Publication year - 2018
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.4009
Subject(s) - space (punctuation) , monte carlo method , mathematics , infinity , upper and lower bounds , energy (signal processing) , combinatorics , radius , computer science , mathematical analysis , statistics , operating system , computer security
We prove optimal lower bounds for the growth of the potential energy over balls of minimizers to the vectorial Allen–Cahn energy in two spatial dimensions, as the radius tends to infinity. Copyright © 2016 John Wiley & Sons, Ltd.