Oblique derivative problems for elliptic equations

PDE Seminar
Tuesday, December 2, 2008 - 3:15pm for 1.5 hours (actually 80 minutes)
Skiles 255
Gary M. Lieberman – Iowa State University
Michael Westdickenberg
The usual boundary condition adjoined to a second order elliptic equation is the Dirichlet problem, which prescribes the values of the solution on the boundary. In many applications, this is not the natural boundary condition. Instead, the value of some directional derivative is given at each point of the boundary. Such problems are usually considered a minor variation of the Dirichlet condition, but this talk will show that this problem has a life of its own. For example, if the direction changes continuously, then it is possible for the solution to be continuously differentiable up to a merely Lipschitz boundary. In addition, it's possible to get smooth solutions when the direction changes discontinuously as well.