A new fundamental inequality yields W^{1,2} regularity of |Du|^{(p-γ)/2}Du for p-harmonic functions and W^{2,q} regularity for elliptic and parabolic p-Laplace equations with sharp ranges of p.
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Second order regularity for elliptic and parabolic equations involving $p$-Laplacian via a fundamental inequality
A new fundamental inequality yields W^{1,2} regularity of |Du|^{(p-γ)/2}Du for p-harmonic functions and W^{2,q} regularity for elliptic and parabolic p-Laplace equations with sharp ranges of p.