TY - CHAP
T1 - Basic applied functional analysis
AU - Assous, Franck
AU - Ciarlet, Patrick
AU - Labrunie, Simon
N1 - Publisher Copyright:
© Springer International Publishing AG, part of Springer Nature 2018.
PY - 2018/1/1
Y1 - 2018/1/1
N2 - To measure data and solutions spatially, we recall a number of useful definitions and results on Lebesgue and standard Sobolev spaces. Then, we introduce more specialized Sobolev spaces, which are better suited to measuring solutions to electromagnetics problems, in particular, the divergence and the curl of fields. This also allows one to measure their trace at interfaces between two media, or on the boundary. Last, we construct ad hoc function spaces, adapted to the study of time- and space-dependent electromagnetic fields.
AB - To measure data and solutions spatially, we recall a number of useful definitions and results on Lebesgue and standard Sobolev spaces. Then, we introduce more specialized Sobolev spaces, which are better suited to measuring solutions to electromagnetics problems, in particular, the divergence and the curl of fields. This also allows one to measure their trace at interfaces between two media, or on the boundary. Last, we construct ad hoc function spaces, adapted to the study of time- and space-dependent electromagnetic fields.
U2 - 10.1007/978-3-319-70842-3_2
DO - 10.1007/978-3-319-70842-3_2
M3 - Chapter
AN - SCOPUS:85067973327
T3 - Applied Mathematical Sciences (Switzerland)
SP - 73
EP - 105
BT - Applied Mathematical Sciences (Switzerland)
PB - Springer
ER -