On the sets of image-regularity of solutions for a class of degenerate nonlinear problems with slightly regular data Original Research Article

We consider the Dirichlet problem for a class of degenerate nonlinear elliptic fourth-order equations in divergence form. Coefficients of the equations satisfy a strengthened ellipticity condition involving two weighted functions. The right-hand sides F(x,u)F(x,u) of the equations depend on the unknown function uu. Under some conditions, including LmLm-regularity of F(⋅,0)F(⋅,0) with mm close to 1, we establish that the problem under consideration has a WW-solution bounded on the sets where the behaviour of the data of the problem is regular enough.