| Abstract: |
| This talk investigates the optimal regularity for solutions to singular elliptic equations involving the 1-Laplace operator. We analyze a class of problems whose model case is $-\Delta_1 u = f(x)u^{-\gamma}$ with homogeneous Dirichlet boundary conditions. In contrast to the classical $p$-Laplacian case with $p>1$, we prove that the structure of the $1$-Laplacian guarantees global $BV$ regularity of the solutions for any power $\gamma > 0$. We will show how a priori estimates based on truncation arguments allow us to handle the boundary discontinuity issue and to control the effects arising from the domain's curvature. |
|