Landesman–Lazer type conditions and quasilinear elliptic equations
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 over the functions that assume given boundary values ϕ on ∂Ω. The vector field 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...