Abstract
The regularity of the minimizers of a special type of non-isotropic variational minimization problem is studied. The particularity of the potential of energy is that it has different growth rate with respect to different parts of the derivatives of the function. In particular, the model treated in this paper can be described as
By using a result of P.Marcellini (cf. [4]) and perturbation method, it is proved that the minimizer of the Dirichlet boundary value problem is a function of W 1, ∞loc .
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Qi, T. Regularity of minimizers of non-isotropic integrals of the calculus of variations. Annali di Matematica pura ed applicata 164, 77–87 (1993). https://doi.org/10.1007/BF01759315
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DOI: https://doi.org/10.1007/BF01759315