| Abstract: |
| In this talk, I will present a new $L^\infty$ bound for solutions to the Poisson problem associated with the weighted $1$-Laplacian. This estimate is analogous to the classical result for uniformly elliptic equations established independently by Aleksandrov, Bakelman, and Pucci in the 1960s, and it is based on an analysis of the contact set of the solutions and their quasiconcave envelopes. |
|