| Wednesday, 19.03.2025 | |
| Type | seminar in the framework of the PDE Afternoon |
| Time | 15:30 - 16:00 |
| Place | University of Vienna, Faculty of Mathematics, Oskar-Morgenstern-Platz 1, Vienna (map) |
| Room | HS 2, ground floor - how to get there |
| Speaker | (TU Wien) |
| Title | Helmholtz decompositions in broken Sobolev spaces |
| Abstract | One version of the classical Helmholtz decomposition states that every vector field v∈H(curl) can be decomposed into a more regular vector field and a gradient field.
We extend this result by considering vector fields v that are piecewise regular and satisfy certain transmission conditions across surfaces of discontinuity. We show that such a v can be decomposed in a vector field w that is piecewise even more regular than v and either a gradient field ∇ψ or a solenoidal field curlz. Finally, we apply these findings to derive wavenumber-explicit regularity estimates for Maxwell's equations in piecewise smooth media. |
| Notes | This event takes place in hybrid form (in person and online on Zoom). Slides and additional materials are available on the Moodle service of the University of Vienna. If you want additional details (for example, if you want to attend an event online and would like to receive the Zoom link), please write an email to matteo.tommasini@univie.ac.at. Further details are available at this link. |
| Attachment | link |
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