We show optimal existence, nonexistence and regularity results for nonnegative solutions to Dirichlet problems as - δ1u = g(u)|Du| + h(u)fin ω,u = 0 on ℓω, where ω is an open bounded subset of RN, f ≥ 0 belongs to LN(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.
1-Laplacian type problems with strongly singular nonlinearities and gradient terms / Giachetti, D.; Oliva, F.; Petitta, F.. - In: COMMUNICATIONS IN CONTEMPORARY MATHEMATICS. - ISSN 0219-1997. - 24:10(2022), p. 2150081. [10.1142/S0219199721500814]
1-Laplacian type problems with strongly singular nonlinearities and gradient terms
Oliva F.;
2022
Abstract
We show optimal existence, nonexistence and regularity results for nonnegative solutions to Dirichlet problems as - δ1u = g(u)|Du| + h(u)fin ω,u = 0 on ℓω, where ω is an open bounded subset of RN, f ≥ 0 belongs to LN(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.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
