Structural stability for variable exponent elliptic problems, I: The image-Laplacian kind problems Original Research Article

We study the structural stability (i.e., the continuous dependence on coefficients) of solutions of the elliptic problems under the form View the MathML sourceb(un)−divan(x,∇un)=fn. Turn MathJax on The equation is set in a bounded domain View the MathML sourceΩ of RNRN and supplied with the homogeneous Dirichlet boundary condition on View the MathML source∂Ω. Here bb is a non-decreasing function on RR, and (an(x,ξ))n(an(x,ξ))n is a family of applications which verifies the classical Leray–Lions hypotheses but with a variable summability exponent pn(x)pn(x), 1