Variational forms for the inverses of integral logarithmic operators over an interval
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Date
2011
Journal Title
Journal ISSN
Volume Title
Publisher
ELSEVIER FRANCE-EDITIONS SCIENTIFIQUES MEDICALES ELSEVIER
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 Calderon-type identities in each case. (C) 2011 Academie des sciences. Published by Elsevier Masson SAS. All rights reserved.
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Keywords
NUMERICAL-SOLUTION, EQUATIONS