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Everywhere regularity for vectorial functionals with general growth. (English) Zbl 1066.49023

Summary: We prove Lipschitz continuity for local minimizers of integral functionals of the Calculus of Variations in the vectorial case, where the energy density depends explicitly on the space variables and has general growth with respect to the gradient. One of the models is \[ F(u)=\int_{\Omega }a(x)[h\left (| Du| \right )]^{p(x)}\,dx \] with \(h\) a convex function with general growth (also exponential behaviour is allowed).

MSC:

49N60 Regularity of solutions in optimal control
35J50 Variational methods for elliptic systems
49J10 Existence theories for free problems in two or more independent variables
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