A regularity result for polyharmonic variational inequalities with thin obstacles
We prove higher integrability for the gradient of bounded minimizers of some variational integrals with anisotropic growth.
Using a perturbation argument based on a finite dimensional reduction, we find positive solutions to a given class of perturbed degenerate elliptic equations with critical growth.
We prove a formula relating the index of a solution and the rotation number of a certain complex vector along bifurcation diagrams.