Abstract
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.
Translated title of the contribution | Variational forms for the inverses of integral logarithmic operators over an interval |
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Original language | French |
Pages (from-to) | 547-552 |
Number of pages | 6 |
Journal | Comptes Rendus Mathematique |
Volume | 349 |
Issue number | 9-10 |
DOIs | |
State | Published - May 2011 |
Externally published | Yes |