The classical problem of the calculus of variations in the autonomous case: Relaxation and Lipschitzianity of solutions
From MaRDI portal
Publication:4429753
DOI10.1090/S0002-9947-03-03347-6zbMath1064.49027MaRDI QIDQ4429753
Publication date: 28 September 2003
Published in: Transactions of the American Mathematical Society (Search for Journal in Brave)
Regularity of solutions in optimal control (49N60) Methods involving semicontinuity and convergence; relaxation (49J45)
Related Items
Some regularity properties on Bolza problems in the calculus of variations, Relaxation and nonoccurrence of the Lavrentiev phenomenon for nonconvex problems, Unnamed Item, The existence of solutions to variational problems of slow growth, Lipschitzianity of optimal trajectories for the Bolza optimal control problem, Lipschitz regularity of the minimizers of autonomous integral functionals with discontinuous non-convex integrands of slow growth, Some problems in the calculus of variations, Non-occurrence of gap for one-dimensional non-autonomous functionals, Existence of Lipschitzian solutions to the classical problem of the calculus of variations in the autonomous case, Lipschitz Continuity of Optimal Trajectories in Deterministic Optimal Control, Regularity of Solutions for the Autonomous Integrals of the Calculus of Variations, Necessary and sufficient conditions for optimality of nonconvex, noncoercive autonomous variational problems with constraints, Normality of the maximum principle for nonconvex constrained Bolza problems, Necessary conditions and non-existence results for autonomous nonconvex variational problems, Lipschitz regularity for minima without strict convexity of the Lagrangian, Existence of vector minimizers for nonconvex 1-dim integrals with almost convex Lagrangian, The basic problem of the calculus of variations: Du Bois-Reymond equation, regularity of minimizers and of minimizing sequences, Equi-Lipschitz minimizing trajectories for non coercive, discontinuous, non convex Bolza controlled-linear optimal control problems, Relaxation and regularity in the calculus of variations, Existence of minimizers of free autonomous variational problems via solvability of constrained ones, Another theorem of classical solvability `in small' for one-dimensional variational problems, On Lipschitz regularity of minimizers of a calculus of variations problem with non locally bounded Lagrangians, A new variational inequality in the calculus of variations and Lipschitz regularity of minimizers, A Du Bois-Reymond convex inclusion for nonautonomous problems of the calculus of variations and regularity of minimizers, Unnamed Item, Regularity of solutions to higher-order integrals of the calculus of variations, A relaxation result for autonomous integral functionals with discontinuous non-coercive integrand, Monotonicity properties of minimizers and relaxation for autonomous variational problems, Existence and Lipschitz regularity of solutions to Bolza problems in optimal control, Coercivity of integral functionals with non-everywhere superlinear Lagrangians, On a new necessary condition in the calculus of variations for Lagrangians that are highly discontinuous in the state and velocity, Non-coercive radially symmetric variational problems: existence, symmetry and convexity of minimizers, Uniform boundedness for the optimal controls of a discontinuous, non-convex Bolza problem,
Cites Work
- Unnamed Item
- Lipschitz regularity for minimizers of integral functionals with highly discontinuous integrands
- One-dimensional variational problems whose minimizers do not satisfy the Euler-Lagrange equation
- Reparametrizations and approximate values of integrals of the calculus of variations.
- On the minimum problem for a class of non-coercive functionals
- Regularity Properties of Solutions to the Basic Problem in the Calculus of Variations
- A General Chain Rule for Derivatives and the Change of Variables Formula for the Lebesgue Integral
- Convex Analysis
