[Formulations variationnelles pour les inverses des opérateurs intégraux logarithmiques définis sur un intervalle]
Nous présentons des formulations variationnelles explicites et exactes pour les opérateurs intégraux faiblement singulier et hyper-singulier définis sur un interval borné ainsi que pour leurs inverses. En décomposant les solutions en parties symétriques et anti-symétriques, nous caractérisons les espaces de Sobolev associés et retrouvons des identités du type Calderón dans chaque cas.
We present explicit and exact variational formulations for the weakly singular and hypersingular operators over an interval as well as for their corresponding inverses. By decomposing the solutions in symmetric and antisymmetric parts, we precisely characterize the associated Sobolev spaces. Moreover, we are able to define novel Calderón-type identities in each case.
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@article{CRMATH_2011__349_9-10_547_0,
author = {Jerez-Hanckes, Carlos and N\'ed\'elec, Jean-Claude},
title = {Variational forms for the inverses of integral logarithmic operators over an interval},
journal = {Comptes Rendus. Math\'ematique},
pages = {547--552},
publisher = {Elsevier},
volume = {349},
number = {9-10},
year = {2011},
doi = {10.1016/j.crma.2011.01.016},
language = {en},
url = {http://www.numdam.org/articles/10.1016/j.crma.2011.01.016/}
}
TY - JOUR AU - Jerez-Hanckes, Carlos AU - Nédélec, Jean-Claude TI - Variational forms for the inverses of integral logarithmic operators over an interval JO - Comptes Rendus. Mathématique PY - 2011 SP - 547 EP - 552 VL - 349 IS - 9-10 PB - Elsevier UR - http://www.numdam.org/articles/10.1016/j.crma.2011.01.016/ DO - 10.1016/j.crma.2011.01.016 LA - en ID - CRMATH_2011__349_9-10_547_0 ER -
%0 Journal Article %A Jerez-Hanckes, Carlos %A Nédélec, Jean-Claude %T Variational forms for the inverses of integral logarithmic operators over an interval %J Comptes Rendus. Mathématique %D 2011 %P 547-552 %V 349 %N 9-10 %I Elsevier %U http://www.numdam.org/articles/10.1016/j.crma.2011.01.016/ %R 10.1016/j.crma.2011.01.016 %G en %F CRMATH_2011__349_9-10_547_0
Jerez-Hanckes, Carlos; Nédélec, Jean-Claude. Variational forms for the inverses of integral logarithmic operators over an interval. Comptes Rendus. Mathématique, Tome 349 (2011) no. 9-10, pp. 547-552. doi : 10.1016/j.crma.2011.01.016. http://www.numdam.org/articles/10.1016/j.crma.2011.01.016/
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