1-Laplacian type problems with strongly singular nonlinearities and gradient terms

Abstract

We show optimal existence, nonexistence and regularity results for nonnegative solutions to Dirichlet problems aswhere Ω is an open bounded subset of R N , f ≥ 0 belongs to L N (Ω), and g and h are continuous functions that may blow up at zero. As a noteworthy fact we show how a non-trivial interaction mechanism between the two nonlinearities g and h produces remarkable regularizing effects on the solutions. The sharpness of our main results is discussed through the use of appropriate explicit examples.