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If $1 \gamma_c$ at some point $a\in\Omega$, that is, $F(x)\simeq|x-a|^{; ; -\gamma}; ; $ in a neighbourhood of $a$, then at the same point the weak solution $u$ has singularity of order which is larger than $\gamma$. The value of $\gamma_c$ is optimal. For $p>2$ we have the loss of regularity in the sense that if $F(x)=C|x|^m$ with $m>0$, then $u(x)=u(0)+D|x|^{; ; \mu}; ; $ with $\mu \gamma_c$. We show that the $p$-Laplace operator is not hypoelliptic for $p\in(1, \infty)\setminus\{; ; 1+1/n:n\in2\mathbb{; ; N}; ; -1\}; ; $.

Loss of regularity of weak solutions of p-Laplace equations for p≠2