Existence of vector minimizers for nonconvex 1-dim integrals with almost convex Lagrangian

[摘要] This paper proves new results of existence of minimizers for the nonconvex integral integral(b)(a) L(x, x') dt, among the AC functions x: [a,b] --> R-n with x(a) = A, x(b) = B. Our Lagrangian L(.) is e.g. 1sc with superlinear growth, assuming +infinity values freely. We replace convexity by almost convexity, a hypothesis which in the radial superlinear case L(s,xi) = f(s, vertical bar xi vertical bar) is automatically satisfied provided f(s, .) is convex at zero. (C) 2007 Elsevier Inc. All rights reserved.

[发布日期] 2007-12-15

[效力级别]  Proceedings Paper

[关键词] calculus of variations;nonconvex nonlinear integrals;regularity