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Euler-Lagrange and Hamiltonian formalisms in variational problems involving differential inclusions

Speaker: 
Alexander Ioffe Technion-Israel Institute of Technology, Haifa, Israel
Institution: 
Schedule: 
Wednesday, March 17, 1999 - 06:30 to 07:30
Location: 
room L
Abstract: 

Analysis of variational problems involving differential inclusions dx/dt \in F(t, x) is inevitably connected with nonsmoothness unless the set-valued mapping F admits a smooth parametrization. Still it appears possible to develop a theory of necessary conditions for such problems containing the corresponding classical results and, moreover, extending the Hamiltonian formalism of calculus of variations to such problems. In the talk we mainly discuss the following questions: (a) what is the analogue of the Euler-Lagrange equation for variational problems with differential inclusions? (b) what is the analogue of the Hamiltonian necessary condition for such problems? (c) how Euler-Lagrange and Hamiltonian conditions are connected? We shall also discuss (if time permits) extensions for differential inclusions involving partial differential operators and/or some problems which remain open.

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