We find conditions, in multi-objective convex programming with nonsmooth functions, when the sets of efficient (Pareto) and properly efficient solutions coincide. This occurs, in particular, when all functions have locally flat surfaces (LFS). In the absence of the LFS property the two sets are generally different and the characterizations of efficient solutions assume an asymptotic form for problems with three or more variables. The results are applied to a problem in highway construction, where...

We establish a local Lipschitz regularity result for local minimizers of asymptotically convex variational integrals.

We establish a local Lipschitz regularity result for local minimizers of asymptotically convex variational integrals.

The object of this paper is to prove existence and regularity results for non-linear elliptic differential-functional equations of the form $\mathrm{div}a\left(\nabla u\right)+F\left[u\right]\left(x\right)=0,$ over the functions $u\in W^{1,1}\left(\Omega \right)$ that assume given boundary values ϕ on ∂Ω. The vector field $a:{ℝ}^n\to {ℝ}^n$ satisfies an ellipticity condition and for a fixed x, F[u](x) denotes a non-linear functional of u. In considering the same problem, Hartman and Stampacchia [Acta Math.115 (1966) 271–310] have obtained existence results in the space of uniformly Lipschitz continuous functions...

We prove a lower semicontinuity result for variational integrals associated with a given first order elliptic complex, extending, in this general setting, a well known result in the case ${}^{\text{'}}(ℝⁿ,ℝ){\to }^{\nabla }\text{'}(ℝⁿ,ℝⁿ){\to }^{curl}\text{'}(ℝⁿ,{ℝ}^{n\times n})$.