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AbstractWe investigate weighted elliptic equations containing a convection term with variable exponents that are subject to Dirichlet or Neumann boundary condition. By employing the De Giorgi iteration and a localization method, we give a-priori bounds for solutions to these problems. The existence of solutions is also established using Brezis' theorem for pseudomonotone operators.doi:10.1515/anona-2015-0177 fatcat:tj7subxasbaj5ohnum4xxdv52a