Affiliations: Departament d'Anàlisi Matemàtica, Universitat de València, Burjassot, Valencia, Spain. E-mail: sergio.segura@uv.es | Dipartimento di Matematica, Università di Roma “La Sapienza”, Roma, Italy. E-mail: dallaglio@mat.uniroma1.it
Note: [] Corresponding author: Andrea Dall'Aglio, Dipartimento di Matematica, Università di Roma “La Sapienza”, Piazzale Aldo Moro 5, I-00185 Roma, Italy. E-mail: dallaglio@mat.uniroma1.it.
Abstract: In this paper, we study the Dirichlet problem for an elliptic equation, in which the 1-Laplacian operator and lower-order terms appear. We introduce a suitable definition of solution and prove the existence of, at least, one bounded solution in BV(Ω) having a negligible jump part. Moreover, a uniqueness result for small positive data is proved, and explicit examples of solutions are shown.
Keywords: 1-Laplacian, gradient term with natural growth, degenerate elliptic equations, functions of bounded variations
