Self‐improving property for certain degenerate functionals with generalized Orlicz growth

We investigate a self‐improving property of variational integrals in a weighted framework under generalized Orlicz growth conditions. Assuming that the weight belongs to an appropriate Muckenhoupt class and the growth function satisfies standard structural conditions, we prove that the gradient of any local quasi‐minimizer has local higher integrability. In addition, we establish the existence of minimizers for the associated functional.