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Please use this identifier to cite or link to this item:
http://hdl.handle.net/10174/9800
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Title: | Overview on the Pointwise Constrained Liapunov Vectorial Convexity Theorem |
Authors: | Carlota, Clara Chá, Sílvia Ornelas, António |
Editors: | Datta, B. Frederico, G. S. F. Martins, N. Torres, D. F. M. Zaslavski, A. J. |
Keywords: | Liapunov convexity theorem for single integrals Nonconvex differential inclusions Pointwise constraints Convexity of the range of vector measures |
Issue Date: | 24-Sep-2013 |
Publisher: | Hindawi Publishing |
Citation: | Clara Carlota, Sílvia Chá, and António Ornelas, Overview on the Pointwise Constrained Liapunov Vectorial
Convexity Theorem, Hindawi Publishing Corporation
Conference Papers in Mathematics
Volume 2013, Article ID 353460, 4 pages, http://dx.doi.org/10.1155/2013/353460 (This Conference Paper is based on a presentation given by Clara Carlota and Sílvia Chá at “The CapeVerde InternationalDays on
Mathematics 2013” held from 22 April 2013 to 25 April 2013 in Praia, Cape Verde. Guest Editors: Delfim F. M. Torres, Biswa N. Datta, Gastão S. F. Frederico, Natália Martins, and Alexander J. Zaslavski) |
Abstract: | In applications of the Calculus of Variations, Optimal Control and Differential Inclusions, very important real-life problems are nonconvex vectorial and subject to pointwise constraints. The classical Liapunov convexity theorem is a crucial tool allowing
researchers to solve nonconvex vectorial problems involving single integrals. However, the possibility of extending such theorem
so as to deal with pointwise constraints has remained an open problem for two decades, in the more realistic case using variable
vectorial velocities.We have recently solved it, in the sense of proving necessary conditions and sufficient conditions for solvability of such problem. A quick overview of our results is presented here, the main point being that, somehow, convex constrained
nonuniqueness a.e. implies nonconvex constrained existence. |
URI: | http://hdl.handle.net/10174/9800 |
Type: | article |
Appears in Collections: | CIMA - Artigos em Livros de Actas/Proceedings
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