We show optimal existence, nonexistence and regularity results for nonnegative solutions to Dirichlet problems with nonlinearities that may blow up at zero also in the first order term. 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, Daniela; Oliva, Francescantonio; Petitta, Francesco. - In: COMMUNICATIONS IN CONTEMPORARY MATHEMATICS. - ISSN 0219-1997. - 24:10(2022). [10.1142/S0219199721500814]
1-Laplacian type problems with strongly singular nonlinearities and gradient terms
Daniela Giachetti;Francescantonio Oliva;Francesco Petitta
2022
Abstract
We show optimal existence, nonexistence and regularity results for nonnegative solutions to Dirichlet problems with nonlinearities that may blow up at zero also in the first order term. 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| File | Dimensione | Formato | |
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