Direct methods in variational field theory

DOI10.1134/S0037446622050056zbMath1502.49002OpenAlexW4300594497MaRDI QIDQ2088623

Richard Gratwick, Mikhail A. Sychev

Publication date: 6 October 2022

Published in: Siberian Mathematical Journal (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1134/s0037446622050056

zbMATH Keywords

Euler equationdirect methodminimizerintegral functionalellipticitysingular extremalWeierstras-Hilbert field theory

Mathematics Subject Classification ID

Optimality conditions for free problems in one independent variable (49K05) Existence theories for optimal control problems involving relations other than differential equations (49J21)

Cites Work

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• Regularity theory for one-dimensional variational problems with singular ellipticity
• Pathological solutions to the Euler-Lagrange equation and existence/regularity of minimizers in one-dimensional variational problems
• Another theorem of classical solvability `in small' for one-dimensional variational problems
• Existence and regularity in the small in the calculus of variations
• One-dimensional variational problems whose minimizers do not satisfy the Euler-Lagrange equation
• Variational field theory from the point of view of direct methods
• On the regularity of solutions of one-dimensional variational obstacle problems
• Regularity Properties of Solutions to the Basic Problem in the Calculus of Variations
• ON THE QUESTION OF REGULARITY OF THE SOLUTIONS OF VARIATIONAL PROBLEMS
• A condition on the value function both necessary and sufficient for full regularity of minimizers of one-dimensional variational problems

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