Regularity for nonlocal problems with non-standard growth

Regularity Results for a Class of Obstacle Problems under Non Standard Growth Conditions

We prove regularity results for minimizers of functionals F(u, Ω) := Ω f(x, u, Du) dx in the class K := {u ∈ W 1,p(x)(Ω,R) : u ≥ ψ}, where ψ : Ω → R is a fixed function and f is quasiconvex and fulfills a growth condition of the type L−1|z|p(x) ≤ f(x, ξ, z) ≤ L(1 + |z|p(x)), with growth exponent p : Ω → (1,∞).

Regularity Conditions for Non-Differentiable Infinite Programming Problems using Michel-Penot Subdifferential

In this paper we study optimization problems with infinite many inequality constraints on a Banach space where the objective function and the binding constraints are locally Lipschitz‎. ‎Necessary optimality conditions and regularity conditions are given‎. ‎Our approach are based on the Michel-Penot subdifferential.

Regularity of Minimizers of Integrals of the Calculus of Variations with Non Standard Growth Conditions

Nonlocal Problems at Nearly Critical Growth

We study the asymptotic behavior of solutions to the nonlocal nonlinear equation (−∆p) u = |u|u in a bounded domain Ω ⊂ R as q approaches the critical Sobolev exponent p∗ = Np/(N − ps). We prove that ground state solutions concentrate at a single point x̄ ∈ Ω and analyze the asymptotic behavior for sequences of solutions at higher energy levels. In the semi-linear case p = 2, we prove that for s...

Regularity results for nonlocal equations by approximation

We obtain C regularity estimates for nonlocal elliptic equations that are not necessarily translation invariant using compactness and perturbative methods and our previous regularity results for the translation invariant case.