Note on an elementary inequality and its application to the regularity of p-harmonic functions
We study the Sobolev regularity of \(p\)-harmonic functions. We show that \(|Du|^p-2+s2 Du\) belongs to the Sobolev space \(W^1,2_loc \), \(s>-1-p-1n-1\), for any \(p\)-harmonic function \(u\). The proof is based on an elementary inequality. , number=1, journal=Annales Fennici Mathematici, author=Sarsa, Saara, year=2021, month=Dec., pages=139–153