03.07.2014, 16:15 Uhr  –  Albert Einstein Institut Potsdam, Room 0.01
Seminar "Topics in Geometric Analysis"

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.

 
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