On a class of nonlocal problems with fractional gradient constraint - Azevedo, Assis (2023)
We consider a Hilbertian and a charges approach to fractional gradient constraint problems of the type |D^σ u|≤ g, involving the distributional fractional Riesz gradient D^σ, 0 < σ < 1, extending previous results on the existence of solutions and Lagrange multipliers of these nonlocal problems. We also prove their convergence as σ\nearrow 1 towards their local counterparts with the gradient constraint |Du|≤ g.