Existence and regularity for scalar minimizers of affine nonconvex simple integrals

  • Authors:
  • António Ornelas

  • Affiliations:
  • Centro de Investigação em Matemática e Aplicações da Universidade de Évora (Cima-ue) rua Romão Ramalho 59, P-7000-671 Évora, Portugal

  • Venue:
  • Nonlinear Analysis: Theory, Methods & Applications
  • Year:
  • 2003

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Abstract

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.