Existence and Global Higher Integrability of Quasiminimizers among Minimizing Sequences of Variational Integrals

Quasiminimizers can be viewed as the perturbations of minimizers of variational integrals. We first establish the existence of good minimizing sequences of non-trivial variational integrals containing quasiminimizers of an inhomogeneous p-Dirichlet integral. Employing the concept of variational capacity, we show that the gradients of these quasiminimizers possess global higher integrability.