Direct methods in the calculus of variations
Direct methods in the calculus of variations
A Nonconvex Variational Problem with Constraints
SIAM Journal on Control and Optimization
Genericity and existence of a minimum for scalar integral functionals
Journal of Optimization Theory and Applications
Convex analysis and variational problems
Convex analysis and variational problems
Existence and regularity for scalar minimizers of affine nonconvex simple integrals
Nonlinear Analysis: Theory, Methods & Applications
Existence and regularity for scalar minimizers of affine nonconvex simple integrals
Nonlinear Analysis: Theory, Methods & Applications
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Existence of AC minimizers x: [a, b] → R is proved for the nonconvex integral ∫ab{ρ(x) h(x')+ φ(x)} dt, under the general hypotheses of lower semicontinuity, boundedness below, and superlinear growth at infinity in x'(.). Any nonconvex function h : R → [0, + ∞] will do, provided it is convex at ξ = 0.Moreover, minimizers are shown to satisfy several regularity properties, under adequate hypotheses.