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University of Cambridge > Talks.cam > Geometric Analysis and Partial Differential Equations seminar > $C^{1, \alpha}$ theory for the prescribed mean curvature equation with Dirichlet data

## $C^{1, \alpha}$ theory for the prescribed mean curvature equation with Dirichlet dataAdd to your list(s) Download to your calendar using vCal - Theodora Bourni (AEI, Potsdam)
- Monday 23 February 2009, 16:00-17:00
- CMS, MR13.
If you have a question about this talk, please contact Prof. Mihalis Dafermos. I will discuss regularity of solutions of the prescribed mean curvature equation over a general domain that do not necessarily attain the given boundary data. The work of E.Giusti and others, establishes a very general existence theory of solutions with “unattained Dirichlet data” by minimizing an appropriately defined functional, which includes information about the boundary data. We can naturally associate to such a solution a current, which inherits a natural minimizing property. The main goal is to show that its support is a $C{1,\alpha}$ manifold-with-boundary, with boundary equal to the prescribed boundary data, provided that both the initial domain and the prescribed boundary data are of class $C^{1,\alpha}$. Furthermore, as a consequence, I will discuss some interesting results about the trace of such a solution; in particular for a large class of boundary data with jump discontinuities, the trace has a jump discontinuity along which it attaches to the vertical part of the prescribed boundary. This talk is part of the Geometric Analysis and Partial Differential Equations seminar series. ## This talk is included in these lists:- All CMS events
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