Existence of scalar minimizers for nonconvex simple integrals of sum type
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Publication:1269087
DOI10.1006/jmaa.1998.5915zbMath0920.49026OpenAlexW1978252484MaRDI QIDQ1269087
Publication date: 15 August 1999
Published in: Journal of Mathematical Analysis and Applications (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1006/jmaa.1998.5915
Methods involving semicontinuity and convergence; relaxation (49J45) Optimization of shapes other than minimal surfaces (49Q10)
Related Items (11)
Lipschitz and piecewise-\(C^{1}\) regularity for scalar minimizers of affine simple integrals ⋮ Existence of scalar minimizers for simple convex integrals with autonomous Lagrangian measurable on the state variable ⋮ Constructive decomposition of any \(L^1(a, b)\) function as sum of a strongly convergent series of integrable functions each one positive or negative exactly in open sets ⋮ An Overview on Existence of Vector Minimizers for Almost Convex 1—dim Integrals ⋮ Necessary and sufficient conditions for optimality of nonconvex, noncoercive autonomous variational problems with constraints ⋮ Existence of vector minimizers for nonconvex 1-dim integrals with almost convex Lagrangian ⋮ Nonconvex minimization problems for functionals defined on vector valued functions ⋮ 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 ⋮ Monotonicity properties of minimizers and relaxation for autonomous variational problems ⋮ Existence and regularity for scalar minimizers of affine nonconvex simple integrals.
Cites Work
- Lipschitz regularity for minimizers of integral functionals with highly discontinuous integrands
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- Théoremes d'existence pour des problèmes du calcul des variations du type: \(\text{Inf}\int^L_0f(x,u'(x))dx\) et \(\text{Inf} \int^L_0f(x,u(x),u'(x))dx\).
- Continuous selections and differential relations
- Genericity and existence of a minimum for scalar integral functionals
- The Existence Question in the Calculus of Variations: A Density Result
- On the range of an unbounded vector-valued measure
- State Constraints in Convex Control Problems of Bolza
- Direct methods in the calculus of variations
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