We prove some interpolation inequalities which arise in the analysis of pattern formation in physics. They are the strong version of some already known estimates in weak form that are used to give a lower bound of the energy in many contexts (coarsening and branching in micromagnetics and superconductors). The main ingredient in the proof of our inequalities is a geometric construction which was first used by Choksi, Conti, Kohn, and one of the authors in the study of branching in superconductors.
Cinti E, Otto F (2016). Interpolation inequalities in pattern formation. JOURNAL OF FUNCTIONAL ANALYSIS, 271, 3348-3392 [10.1016/j.jfa.2016.05.007].
Interpolation inequalities in pattern formation
CINTI, ELEONORA;
2016
Abstract
We prove some interpolation inequalities which arise in the analysis of pattern formation in physics. They are the strong version of some already known estimates in weak form that are used to give a lower bound of the energy in many contexts (coarsening and branching in micromagnetics and superconductors). The main ingredient in the proof of our inequalities is a geometric construction which was first used by Choksi, Conti, Kohn, and one of the authors in the study of branching in superconductors.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
