Density estimates for vector minimizers and applications

Nicholas D.  Alikakos; Giorgio  Fusco

doi:10.3934/dcds.2015.35.5631

Article Contents

2015, Volume 35, Issue 12: 5631-5663. Doi: 10.3934/dcds.2015.35.5631

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Density estimates for vector minimizers and applications

Nicholas D. Alikakos^1, and
Giorgio Fusco^2,

1.
Department of Mathematics, University of Athens, Panepistemiopolis, 15784 Athens
2.
Università degli Studi dell'Aquila, Via Vetoio, 67010 Coppito, L'Aquila

Received: April 2014

Revised: September 2014

Published: December 2015

Abstract / Introduction Related Papers Cited by

Abstract

We extend the Caffarelli--Córdoba estimates to the vector case (L. Caffarelli and A. Córdoba, Uniform Convergence of a singular perturbation problem, Comm. Pure Appl. Math. 48 (1995)). In particular, we establish lower codimension density estimates. These are useful for studying the hierarchical structure of minimal solutions. We also give applications.

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Mathematics Subject Classification: 35J20, 35J47, 35J50.

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