On the zeros of solutions of elliptic inequalities in bounded domains

AbstractA generalized Sturmian theorem is proved for elliptic differential inequalities of second order in arbitrary bounded domains G in n-dimensional Euclidean space. Under weaker hypotheses than normally given, no boundary regularity is required for the conclusion that every solution of such an inequality has a zero in G. This is a so-called strong theorem, meaning that the conclusion applies to G rather than Ḡ. Specialization to linear symmetric elliptic equations sharpens earlier Sturmian theorems