Abstract
We study variational problems for the functional F(u) = ∫Ω f(x, u(x), Lu(x)) dx where u∈uo + V, with Vbeing any closed linear subspace of W2.P(Ω) containing W2.p.0(Ω), Ω is a bounded open set, p > 1, L is a differential operator of second order. We determine the greatest lower semicontinuous function majorised by F for the weak topology of W2.p, for its sequential version if f satisfies no coercivity assumption, showing that in both cases the relaxed functional is expressed in terms of the function ξ↦ f**(x, u, ξ). Finally, an existence result in case f (not necessarily convex) depending only on the Laplacian, is given
Publisher
Cambridge University Press (CUP)
Reference25 articles.
1. Elliptic Partial Differential Equations of Second Order
2. Radially symmetric solutions of a class of problems of the calculus of variations without convexity assumptions
3. Théorémes d'existence en optimisation non convexe
4. Régularisation s.c.i., relaxation et théorèmes bang-band;Valadier;C.R. Acad. Sci. Paris Sér. I Math.,1981
5. 18 Flores F. . On radial solutions for non-convex variational problems (To appear in Houston J. Math).).
Cited by
3 articles.
订阅此论文施引文献
订阅此论文施引文献，注册后可以免费订阅5篇论文的施引文献，订阅后可以查看论文全部施引文献