Convex integral functionals
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- by Nikolaos S. Papageorgiou PDF
- Trans. Amer. Math. Soc. 349 (1997), 1421-1436 Request permission
Abstract:
We study nonlinear integral functionals determined by normal convex integrands. First we obtain expressions for their convex conjugate, their $\varepsilon$-subdifferential $(\varepsilon \ge 0)$ and their $\varepsilon$-directional derivative. Then we derive a necessary and sufficient condition for the existence of an approximate solution for the continuous infimal convolution. We also obtain general conditions which guarantee the interchangeability of the conditional expectation and subdifferential operators. Finally we examine the conditional expectation of random sets.References
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Additional Information
- Nikolaos S. Papageorgiou
- Affiliation: Department of Mathematics, National Technical University, Zografou Campus, Athens 15780, Greece
- MR Author ID: 135890
- Received by editor(s): January 13, 1994
- Received by editor(s) in revised form: January 23, 1995
- © Copyright 1997 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 349 (1997), 1421-1436
- MSC (1991): Primary 47H30, 49N15
- DOI: https://doi.org/10.1090/S0002-9947-97-01478-5
- MathSciNet review: 1321585