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Global boundedness for vector valued minimizers of some anisotropic variational integrals

Wang Lianhong, Gao Hongya

This paper deals with anisotropic integral functionals of the type I(u; Ω) = Z Ω f(x, Du(x))dx. We present a monotonicity inequality on the density f(x, ξ) with weight, which guarantees global boundedness of minimizers u with gradient constraints.