Interior regularity for two-dimensional stationary Q-valued maps

2022/11/16 by Jonas Hirsch, Hirsch, Jonas, Luca Spolaor +1 · 1 citation
Mathematics · Computer Science · #Mathematical Dynamics and Fractals #advanced mathematical theories #Advanced Mathematical Modeling in Engineering

paper · pdf · doi:10.48550/arxiv.2211.09052

Abstract

We prove that 2-dimensional Q-valued maps that are stationary with respect to outer and inner variations of the Dirichlet energy are Hölder continuous and that the dimension of their singular set is at most one. In the course of the proof we establish a strong concentration-compactness theorem for equicontinuous maps that are stationary with respect to outer variations only, and which holds in every dimensions.

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• Carleman estimates for stationary Q-valued maps: a variational approach

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