Local \({W^{2,m(\cdot)}_{loc}}\) regularity for \(p\)(.)-Laplace equations (Q1942244)

The paper under review deals with the study of the local regularity of the weak solutions to a class of nonlinear elliptic equations with a variable exponent. Since in general solutions are not of class \(C^2_{loc}\), it is an important issue to study the summability of the second derivatives of the solutions. The main idea in the proof is to linearize the equation and then to exploit it by means of good appropriate test functions. Then there are established some uniform estimates on the second derivatives, which enable the authors to deduce the regularity properties by passing to the limiting problem.