A-priori bounds and existence for solutions of weighted elliptic equations with a convection term

Abstract

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.

Keywords

• weighted variable exponent lebesgue–sobolev spaces
• a-priori bound
• de giorgi iteration
• localization method
• pseudomonotone operators
• 35j20
• 35j60
• 35j70
• 47j10
• 46e35