| Abstract: |
| We derive the sharp vectorial Kato inequality for $p$-harmonic mappings. Surprisingly, the optimal constant differs from the one obtained for scalar valued $p$-harmonic functions. As an application we show how Kato-type inequalities can be used to deduce regularity for $p$-harmonic maps from a three dimensional ball to a three dimensional sphere. Based on joint works with Andreas Gastel, Micha\l Mi\`skiewicz, and Patryk Tokarczuk. |
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