We prove local gradient bounds and interior Hölder estimates for the first derivatives of functions which locally minimize the variational integral subject to the side condition . We establish these results for various classes of integrands with non-standard growth. For example, in the case of smooth the -condition is sufficient. A second class consists of all convex functions with -growth.
Cite this article
M. Bildhauer, Martin Fuchs, Giuseppe Mingione, A Priori Gradient Bounds and Local -Estimates for (Double) Obstacle Problems under Non-Standard Growth Conditions. Z. Anal. Anwend. 20 (2001), no. 4, pp. 959–985DOI 10.4171/ZAA/1054