| Abstract: |
| In this talk, we discuss the existence and qualitative behavior of bounded variation (BV) solutions to Dirichlet problems driven by the 1-Laplace operator. We deal with general, and possibly singular, first-order nonlinearities and we focus on how these nonlinearities play a regularizing effect on the solutions. In particular, we study the role of the gradient nonlinearity in the attainment of the homogeneous boundary condition for the solutions. |
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