Аннотация:
Anisotropic variational integrals of (p,q)-growth are considered. For the scalar case, the interior C1,α-regularity of bounded local minimizers is proved under the assumption that q⩽2p, and a famous counterexample of Giaquinta is discussed. In the vector case, some higher integrability result for the gradient is obtained.
Ключевые слова:
anisotropic problems, regularity of minimizers.
Образец цитирования:
M. Bildhauer, M. Fuchs, X. Zhong, “Variational integrals with a wide range of anisotropy”, Алгебра и анализ, 18:5 (2006), 46–71; St. Petersburg Math. J., 18:5 (2007), 717–736