Optimality conditions for nonsmooth interval-valued and multiobjective semi-infinite programming

We consider a nonsmooth semi-infinite interval-valued vector programming problem, where the objectives and constraints functions need not to be locally Lipschitz. Using Abadie's constraint qualification and convexificators, we provide Karush-Kuhn-Tucker necessary optimality conditions by converting the initial problem into a bi-criteria optimization problem. Furthermore, we establish sufficient optimality conditions under the asymptotic convexity assumption.

Weighted Orlicz regularity estimates for fully nonlinear elliptic equations with asymptotic convexity

We prove interior Hessian estimates in the setting of weighted Orlicz spaces for viscosity solutions of fully nonlinear, uniformly elliptic equations [Formula: see text] under asymptotic assumptions on the nonlinear operator [Formula: see text] The results are further extended to fully nonlinear, asymptotically elliptic equations.

Lipschitz regularity of solutions of some asymptotically convex problems

SynopsisWe prove local Lipschitz regularity for minimisers of integral functionals of the form J(u) = ∫Ω{f(Du(x)) + g(x, u(x))} dx, where the integrand f is not convex but satisfies some asymptotic convexity assumption.