Geodesic
Note on an elementary inequality and its application to the regularity of p-harmonic functions
Saara Sarsa1
1University of Helsinki, Department of Mathematics and Statistics
Annales Fennici Mathematici, Tome 47 (2022) no. 1, pp. 139-153

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We study the Sobolev regularity of $p$-harmonic functions. We show that $|Du|^{\frac{p-2+s}{2}}Du$ belongs to the Sobolev space $W^{1,2}_{\operatorname{loc}}$, $s>-1-\frac{p-1}{n-1}$, for any $p$-harmonic function $u$. The proof is based on an elementary inequality.
DOI : 10.54330/afm.112699
Keywords: p-harmonic function, Sobolev regularity, elementary inequality

Saara Sarsa  1

1 University of Helsinki, Department of Mathematics and Statistics 
Saara Sarsa. Note on an elementary inequality and its application to the  regularity of p-harmonic functions. Annales Fennici Mathematici, Tome 47 (2022) no. 1, pp. 139-153. doi: 10.54330/afm.112699
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