We study the Dirichlet problem for an elliptic equation involving the 1-Laplace operator and a reaction term, namely: 'Equation Presented', where Ω ⊂ ℝN is an open bounded set having Lipschitz boundary, f ∈ L1(Ω) is nonnegative, and h is a continuous real function that may possibly blow up at zero. We investigate optimal ranges for the data in order to obtain existence, nonexistence and (whenever expected) uniqueness of nonnegative solutions.
The Dirichlet problem for the 1-Laplacian with a general singular term and L1-data / Latorre, M.; Oliva, F.; Petitta, F.; De Leon, S. S.. - In: NONLINEARITY. - ISSN 0951-7715. - 34:3(2021), pp. 1791-1816. [10.1088/1361-6544/abc65b]
The Dirichlet problem for the 1-Laplacian with a general singular term and L1-data
Oliva F.;
2021
Abstract
We study the Dirichlet problem for an elliptic equation involving the 1-Laplace operator and a reaction term, namely: 'Equation Presented', where Ω ⊂ ℝN is an open bounded set having Lipschitz boundary, f ∈ L1(Ω) is nonnegative, and h is a continuous real function that may possibly blow up at zero. We investigate optimal ranges for the data in order to obtain existence, nonexistence and (whenever expected) uniqueness of nonnegative solutions.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
