Regularity issues for Cosserat continua and p-harmonic maps

2017/04/28 by Gastel, Andreas
#58E20 #74B20 #74G40 #Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.1704.08856

Abstract

For minimizers in a geometrically nonlinear Cosserat model for micropolar elasticity of continua, we prove interior Hölder regularity, up to isolated singular points that may be possible if the exponent p from the model is 2 or in ((32)/(15),3). The obstacle to full continuity turns out to be the existence of certain minimizing homogeneous p-harmonic maps to S³. For those, we slightly improve existing regularity theorems in order to achieve our result on the Cosserat model.

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