Nonlinear problems with unbounded coefficients and $$L^1$$ data

Abstract

We consider a class of nonlinear elliptic problems whose prototype involves a coefficients matrix blowing up for a finite value m of the unknown u. Since datum is in $$L^1$$ , a suitable notion of renormalized solutions is introduced taking into account that u can reach the value m and the existence of such solutions is proved. We study the corresponding evolution problem as well.