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Partial Expansion of a Lipschtiz Domain

Thursday, June 7, 3:30PM – 5PM
POB 6.304

Weifeng (Frederick) Qiu

We show that a Lipschitz domain can be expanded solely near a part of its boundary, assuming that the part is enclosed by a piecewise C1 curve. The expanded domain as well as the extended part are both Lipschitz. We apply this result to prove a regular decomposition of standard vector Sobolev spaces with vanishing traces only on part of the boundary. Another application in the construction of low-regularity projectors into finite element spaces with partial boundary conditions is also indicated.

This is a joint work with Jay Gopalakrishan.

Hosted by Leszek Demkowicz