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Hölder continuity results for a class of functionals with non-standard growth. (English) Zbl 1178.49045
Summary: We prove regularity results for real valued minimizers of the integral functional \(\int f(x, u, Du)\) under non-standard growth conditions of \(p(x)\)-type, i.e. \[ L^{-1} |z|^{p(x)} \leq f(x, s, z) \leq L(1+ |z|^{p(x)}) \] under sharp assumptions on the continuous function \(p(x) > 1\).

MSC:
49N60 Regularity of solutions in optimal control
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