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

摘要

The local boundedness of local quasi-minimizers of integral functionals with variable exponent anisotropic (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 (x)-Laplace type equations are obtained.