Derivatives with respect to diffeomorphisms and their applications in control theory and geometrical optics

DOI10.1134/S0081543816050217zbMath1351.49007OpenAlexW2469795158MaRDI QIDQ338042

A. A. Uspenskii

Publication date: 3 November 2016

Published in: Proceedings of the Steklov Institute of Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1134/s0081543816050217

zbMATH Keywords

symmetrydiffeomorphismoptimal controlwavefrontgeometrical opticsminimax solutionsingular setfirst-order PDE

Mathematics Subject Classification ID

Nonsmooth analysis (49J52) Existence of solutions for minimax problems (49J35) Existence theories for optimal control problems involving partial differential equations (49J20) Geometric optics (78A05)

Related Items (1)

Identification of the singularity of the generalized solution of the Dirichlet problem for an eikonal type equation under the conditions of minimal smoothness of a boundary set

Cites Work

• Calculation formulas for nonsmooth singularities of the optimal result function in a time-optimal problem
• On the structure of locally Lipschitz minimax solutions of the Hamilton-Jacobi-Bellman equation in terms of classical characteristics
• On the set of limit values of local diffeomorphisms in wavefront evolution
• Construction of a minimax solution for an eikonal-type equation
• Geometry and asymptotics of wavefronts
• Construction of the optimal outcome function for a time-optimal problem on the basis of a symmetry set
• GENERALIZED SOLUTIONS OF THE HAMILTON-JACOBI EQUATIONS OF EIKONAL TYPE. I. FORMULATION OF THE PROBLEMS; EXISTENCE, UNIQUENESS AND STABILITY THEOREMS; SOME PROPERTIES OF THE SOLUTIONS
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