ISem23

Dear Participants of ISem 23,

We have just uploaded the twelth lecture, which you can find at the following link

https://www.mat.tuhh.de/veranstaltungen/isem23/_media/lecture_12.pdf

or in the forum.

This lecture is concerned with the general class of evolutionary equations covered by Picard's theorem again. We seek to incorporate inhomogeneous boundary value problems. Similar to the case of inhomogeneous initial value problems the implementation of boundary value problems can be done with the help of particular right-hand sides $F$.

For this we introduce certain so-called trace spaces and corresponding trace operators that give meaning to the evaluation of functions in $H(\mathrm{div})$ at the boundary.

In order to be independent of the quality of the boundary, we will also introduce an abstract implementation of these trace spaces and compare the notions introduced.

As usual we like to interact with you over the forum provided so please do not hesitate to communicate and discuss misprints, comments, inaccuracies and the like. Also in this lecture we attached an exercise section. We particularly ask the team from Karlsruhe to submit `official' solutions for us to upload.

With the best regards,

the virtual lecturers