(untitled) (Journal of Partial Differential Equations, 2020)
We consider a solution of the semi-linear partial differential equations in higher space dimensions. We show that if there exist two characteristic hypersurface bearing different weak singularities intersect transversally, and another one characteristic hypersurface issues from above intersection, then the solution would be conormal with respect to the union of these surfaces, and satisfy the so-called &#8220sum law&#8221.