Regularity of flat level sets in phase transitions 论文
2009Annals of Mathematics引用 265
Nonlinear Partial Differential EquationsAdvanced Mathematical Modeling in EngineeringGeometric Analysis and Curvature Flows
摘要
We consider local minimizers of the Ginzburg-Landau energy functionaland prove that, if the 0 level set is included in a flat cylinder then, in the interior, it is included in a flatter cylinder.As a consequence we prove a conjecture of De Giorgi which states that level sets of global solutions ofare hyperplanes in dimension n ≤ 8.