Geodesic
$C^{1,\beta}$-partial regularity of $p$-harmonic maps at the free boundary
Bollettino della Unione matematica italiana, Série 8, 5B (2002) no. 1, pp. 79-107.

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We prove the partial $C^{1, \beta}$-regolarity up to the free boundary of the $p$-harmonic maps which minimize the $p$-energy $\int |Du|^{p} \, dx$.
Dimostriamo la $C^{1, \beta}$-regolarità parziale fino alla frontiera libera delle mappe $p$-armoniche che minimizzano la $p$-energia $\int |Du|^{p} \, dx$. 
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Müller, Thomas. $C^{1,\beta}$-partial regularity of $p$-harmonic maps at the free boundary. Bollettino della Unione matematica italiana, Série 8, 5B (2002) no. 1, pp. 79-107. http://geodesic.mathdoc.fr/item/BUMI_2002_8_5B_1_a2/

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