A remark on the regularity of vector-valued mappings depending on two variables which minimize splitting-type variational integrals
نویسندگان
چکیده
We combine a maximum principle for vector-valued mappings established by D’Ottavio, Leonetti and Musciano [DLM] with regularity results from [BF3] and prove the Hölder continuity of the first derivatives for local minimizers u: Ω → RN of splitting-type variational integrals provided Ω is a domain in R2. Roughly speaking, anisotropic variational integrals ∫ Ω F (∇u) dx with integrand F (∇u) of (p, q)-growth for exponents p ≤ q are characterized through a condition of the form
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