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.
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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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