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

Ky Ho, Inbo Sim
2017 Advances in Nonlinear Analysis  
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