Partial regularity for minimizers of splitting-type variational integrals under general growth conditions. - Part 1

Abstract

We consider variational problems of splitting-type, i.e. the density F:\mathbb{R}^{n}\supset\Omega\rightarrow\mathbb{R}^{N} has an additive decomposition into two functions f and g. Assuming power growth conditions with exponents p and q for these functions, Bildhauer and Fuchs [BF2,3] show partial regularity in the general vector case and full regularity for n = 2 in the superquadratic situation. If the functions f and g depend on the modulus, i.e. f(·) = a(|·|) and g(·) = b(|·|), we generalize the statements for splitting-type variational integrals with power growth conditions to the case of N-functions a and b.