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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.

35J60 Nonlinear elliptic equations
35J66 Nonlinear boundary value problems for nonlinear elliptic equations
Full Text: DOI
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