Basic applied functional analysis

Franck Assous; Patrick Ciarlet; Simon Labrunie

doi:10.1007/978-3-319-70842-3_2

Basic applied functional analysis

Franck Assous, Patrick Ciarlet, Simon Labrunie

Research output: Chapter in Book/Report/Conference proceeding › Chapter › peer-review

Abstract

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.

Original language	English
Title of host publication	Applied Mathematical Sciences (Switzerland)
Publisher	Springer
Pages	73-105
Number of pages	33
DOIs	https://doi.org/10.1007/978-3-319-70842-3_2
State	Published - 2018
Externally published	Yes

Publication series

Name	Applied Mathematical Sciences (Switzerland)
Volume	198
ISSN (Print)	0066-5452
ISSN (Electronic)	2196-968X

Bibliographical note

Publisher Copyright:
© Springer International Publishing AG, part of Springer Nature 2018.

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10.1007/978-3-319-70842-3_2

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Basic applied functional analysis

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