The structure of compact sets generating normal domains and removable singularities for the space $L_p^1(D)$

A study is made of the properties of $p$-normal domains in $R^n$ ($1<p<+\infty$), which will be minimal in the Köbe sense or normal in the Grötzsch sense when $n=p=2$. Descriptions are obtained of removable singularities for the space $L_p^1(D)$ and for compact sets generating $p$-normal domains, in terms of the theory of contingencies and $(n-1)$-dimensional bi-Lipschitz $NC_p$-compact sets.