A Regularity Theory for Scalar Local Minimizers of Splitting-Type Variational Integrals
نویسندگان
چکیده
Starting from Giaquinta’s counterexample [Gi] we introduce the class of splitting functionals being of (p, q)-growth with exponents p ≤ q < ∞ and show for the scalar case that locally bounded local minimizers are of class C. Note that to our knowledge the only C-results without imposing a relation between p and q concern the case of two independent variables as it is outlined in Marcellini’s paper [Ma1], Theorem A, and later on in the work of Fusco and Sbordone [FS], Theorem 4.2.
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