Displaying similar documents to “Examples from the calculus of variations. IV. Concluding review”

Examples from the calculus of variations. III. Legendre and Jacobi conditions

Jan Chrastina (2001)

Mathematica Bohemica

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We will deal with a new geometrical interpretation of the classical Legendre and Jacobi conditions: they are represented by the rate and the magnitude of rotation of certain linear subspaces of the tangent space around the tangents to the extremals. (The linear subspaces can be replaced by conical subsets of the tangent space.) This interpretation can be carried over to nondegenerate Lagrange problems but applies also to the degenerate variational integrals mentioned in the preceding...

Regularity results for a class of obstacle problems

Michela Eleuteri (2007)

Applications of Mathematics

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We prove some optimal regularity results for minimizers of the integral functional ∫ f ( x , u , D u ) d x belonging to the class K : = { u ∈ W 1 , p ( Ω ) u ≥ ψ } , where ψ is a fixed function, under standard growth conditions of p -type, i.e. L - 1 | z | p ≤ f ( x , s , z ) ≤ L ( 1 + | z | p ) .