The partial regularity for minimizers of splitting type variational integrals under general growth conditions I. the autonomous case

We consider variational problems of splitting type, i. e., the case where the density F: Rn ⊃ Ω → RN is represented as the sum of two functions f and g. The partial regularity in the general vector case and the full regularity for n = 2 in the superquadratic situation were established by Bildhauer and Fuchs under the power growth condition on exponents p and q for such functions f and g. We consider the case where f and g depend on the modulus, i. e., f(·) = a({pipe} · {pipe}) and g(·) = b({pipe} · {pipe}), and generalize the results for splitting type variational integrals with power growth conditions to the case of N-functions a and b. Bibliography: 19 titles. © 2010 Springer Science+Business Media, Inc.