Mariana Smit Vega Garcia and Guy David
16:15 Uhr | Mariana Smit Vega Garcia (Universität Düsseldorf) | New developments in the lower dimensional obstacle problem
We will describe the lower-dimensional obstacle problem for a uniformly elliptic, divergence form operator with Lipschitz continuous coefficients. We will give an overview of what is known about this problem, new developments and the role of a new monotonicity formula for an appropriate generalization of Almgren's frequency functional in the optimal regularity of the solution. |
17:45 Uhr | Guy David (Université Paris-Sud) | Sets that minimize the $d$-dimensional Hausdorff measure under a
sliding boundary condition
The main point of the lecture should concern regularity properties of minimal or almost minimal sets that satisfy a sliding boundary condition of Plateau type, and in particular near the boundary. We should in particular discuss some monotonicity property of density, and simple applications in low dimensions. |