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Variational composition of a monotone operator and a linear mapping with applications to elliptic PDEs with singular coefficients |
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| Authors: | Teemu Pennanen,Julian P. Revalski,Michel Thé ra |
| Affiliation: | a Department of Management Science, Helsinki School of Economics, PL 1210, 00101 Helsinki, Finland b Institute of Mathematics and Informatics, Bulgarian Academy of Sciences, Acad. G. Bonchev Street, block 8, 1113 Sofia, Bulgaria c Université de Limoges, 123 Avenue A. Thomas, 87060 Limoges, France |
| Abstract: | This paper proposes a regularized notion of a composition of a monotone operator with a linear mapping. This new concept, called variational composition, can be shown to be maximal monotone in many cases where the usual composition is not. The two notions coincide, however, whenever the latter is maximal monotone. The utility of the variational composition is demonstrated by applications to subdifferential calculus, theory of measurable multifunctions, and elliptic PDEs with singular coefficients. |
| Keywords: | Maximal monotone operator Composition Graphical convergence Subdifferential Measurable multifunction Elliptic PDE |
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