High regularity of the solution to the singular elliptic p(⋅)-Laplacian system. (January 2020) - Crispo, Francesca; Grisanti, Carlo R.
Abstract: We study the regularity properties of solutions to the non-homogeneous singular p ( x ) -Laplacian system in a bounded domain of R n . Under suitable restrictions on the range of p ( x ), we construct a W 2, r solution, with r > n, that implies the Hölder continuity of the gradient. Moreover, assuming just p ( x ) ∈ ( 1, 2 ) we prove that the second derivatives belong to L 2 .