Abstract
The local boundedness of local quasi-minimizers of integral functionals with variable exponent anisotropic \({\overrightarrow{p}(x)}\) growth under suitable assumptions is proved. Based on this result, the global boundedness and the Lipschitz continuity of weak solutions of Dirichlet or Neumann boundary value problems for the \({\overrightarrow{p}(x)}\)-Laplace type equations are obtained.
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The research was supported by National Natural Science Foundation of China (10971087).
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Fan, X. Local boundedness of quasi-minimizers of integral functionals with variable exponent anisotropic growth and applications. Nonlinear Differ. Equ. Appl. 17, 619–637 (2010). https://doi.org/10.1007/s00030-010-0072-3
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DOI: https://doi.org/10.1007/s00030-010-0072-3