Sufficiency theorems for local minimizers of the multiple integrals of the calculus of variations

DOI10.1017/S0308210500000822zbMath0980.49019OpenAlexW1999734317MaRDI QIDQ2710423

Ali Taheri

Publication date: 19 February 2002

Published in: Proceedings of the Royal Society of Edinburgh: Section A Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1017/s0308210500000822

zbMATH Keywords

integral functionalsWeierstrass functionlower semicontinuitysufficient conditionslocal minimality

Mathematics Subject Classification ID

Methods involving semicontinuity and convergence; relaxation (49J45) Optimality conditions for problems involving ordinary differential equations (49K15) Optimality conditions for free problems in one independent variable (49K05)

Related Items (9)

Direct approach to the problem of strong local minima in calculus of variations ⋮ A class of extremising sphere-valued maps with inherent maximal tori symmetries in \(\mathbf{SO}(n)\) ⋮ Necessary and sufficient conditions for the strong local minimality of C¹ extremals on a class of non-smooth domains ⋮ Local minimizers of one-dimensional variational problems and obstacle problems ⋮ Boundary regularity and sufficient conditions for strong local minimizers ⋮ Local minimizers and quasiconvexity -- the impact of topology ⋮ Another theorem of classical solvability `in small' for one-dimensional variational problems ⋮ Sufficient conditions for strong local minima: The case of $C^{1}$ extremals ⋮ Stability and local minimality of spherical harmonic twists \(u={\mathbf{Q}}(|x|) x|x|^{-1} \), positivity of second variations and conjugate points on \(\mathbf{SO}(n)\)

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