  A number of different effects of the violation of the Equivalence Principle
(VEP), taken as sub-leading mechanism of neutrino flavor oscillation, are
examined within the framework of the DUNE experiment. We study the possibility
of obtaining a misleading neutrino oscillation parameter region caused by our
unawareness of VEP. Additionally, we evaluate the impact on the measurement of
CP violation and the distinction of neutrino mass hierarchy at DUNE. Besides,
limits on VEP for a wide variety of textures of the matrix that connects
neutrino gravity eigenstates to flavor eigenstates are imposed. An extra-task
of our study is to set limits on Hamiltonian added terms considering different
energy dependencies ($E^n$, with $n=0,1,2,3$) that can be associated to the
usual Lorentz violating terms defined in the Standard Model Extension
Hamiltonian. In order to understand our results, approximated analytical three
neutrino oscillation probability formulae are derived.
