A pointwise constrained version of the Liapunov convexity theorem for single integrals

Carlota, Clara; Chá, Sílvia; Ornelas, António

doi:10.1007/s00030-012-0199-5

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Our General × Pointwise Constrained Liapunov Convexity Theorem1

Introduction1

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Cited by 2 publications

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“…(see our paper [2] for more general definitions of this set). Then the main result (see [2, Theorems 1.2 and 1.4]) of our research is as follows.…”

Section: Our General × Pointwise Constrained Liapunov Convexity Theoremmentioning

confidence: 99%

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Overview on the Pointwise Constrained Liapunov Vectorial Convexity Theorem

Carlota¹,

Chá²,

Ornelas³

2013

Conference Papers in Mathematics

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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.

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“…(see our paper [2] for more general definitions of this set). Then the main result (see [2, Theorems 1.2 and 1.4]) of our research is as follows.…”

Section: Our General × Pointwise Constrained Liapunov Convexity Theoremmentioning

confidence: 99%

“…Here we present a simplified overview of the main results of our recent paper [2], which has improved this Liapunov theorem by again allowing the fulfilment of the boundary conditions (3)-on the global range of this vector measurebut now under an extra pointwise space constraint:…”

Section: Introductionmentioning

confidence: 99%