Twodimensional anisotropic variational problems

Twodimensional Variational Problems With A Wide Range Of Anisotropy

We consider local minimizers u : R 2 ⊃ Ω → R M of the variational integral Ω H(∇u) dx with density H growing at least quadratically and allowing a very large scale of anisotropy. We discuss higher integrability properties of ∇u as well as the differentiability of u in the classical sense. Moreover, a Liouville-type theorem is established.

Hartley Series Direct Method for Variational Problems

The computational method based on using the operational matrix of anorthogonal function for solving variational problems is computeroriented. In this approach, a truncated Hartley series together withthe operational matrix of integration and integration of the crossproduct of two cas vectors are used for finding the solution ofvariational problems. Two illustrative...

Partial Regularity For Higher Order Variational Problems Under Anisotropic Growth Conditions

We prove a partial regularity result for local minimizers u : Rn ⊃ Ω → RM of the variational integral J(u,Ω) = ∫ Ω f(∇ku) dx, where k is any integer and f is a strictly convex integrand of anisotropic (p, q)–growth with exponents satisfying the condition q < p(1 + 2 n). This is some extension of the regularity theorem obtained in [BF2] for the case n = 2.

Variational Formulation of Problems and Variational Methods

Strong convergence for variational inequalities and equilibrium problems and representations

We introduce an implicit method for nding a common element of the set of solutions of systems of equilibrium problems and the set of common xed points of a sequence of nonexpansive mappings and a representation of nonexpansive mappings. Then we prove the strong convergence of the proposed implicit schemes to the unique solution of a variational inequality, which is the optimality condition for ...