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A-priori bounds and existence for solutions of weighted elliptic equations with a convection term. (English) Zbl 1377.35096
Summary: We 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.

MSC:
35J60 Nonlinear elliptic equations
35J66 Nonlinear boundary value problems for nonlinear elliptic equations
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