Local boundedness of quasi-minimizers of integral functionals with variable exponent anisotropic growth and applications

The local boundedness of local quasi-minimizers of integral functionals with variable exponent anisotropic ${overrightarrow{p}(x)}The local boundedness of local quasi-minimizers of integral functionals with variable exponent anisotropic p^?(x){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 p^?(x){overrightarrow{p}(x)}-Laplace type equations are obtained.