Victor Nistor
Department of Mathematics, Penn State University
Elliptic partial differential equations on bonded, smooth domains are by now well understood and are part of the core of main results of pure and applied mathematics. Few, if any at all, real life domains are smooth, however. A real life domain is more likely to have `straight' boundaries (think of an engineer designing a building). The resulting equations on these non-smooth domains behave quite differently, though, from the smooth ones, at least if one uses the common Sobolev spaces. My talk will present a modification of the common Sobolev spaces that makes the two types of domains much more similar. Part of these results is joint work with Bacuta and Zikatanov. My talk will be accessible to graduate students and non-specialists in the field (including mathematically literate non-mathematicians).