We derive local a priori estimates of the Hölder norm of solutions to quasilinear elliptic systems with quadratic nonlinearities in the gradient. We assume higher integrability of solutions and smallness of its BMO norm but the Hölder norm is estimated in terms of BMO norm of the solution under consideration, only.
In this article we produce a refined version of the classical Pohozaev identity in the radial setting. The refined identity is then compared to the original, and possible applications are discussed.
In this paper we prove a regularity result for local minimizers of functionals of the Calculus of Variations of the typewhere Ω is a bounded open set in , u∈(Ω; ), p> 1, n≥ 2 and N≥ 1. We use the technique of difference quotient without the usual assumption on the growth of the second derivatives of the function f. We apply this result to give a bound on the Hausdorff dimension of the singular set of minimizers.
We examine the p-harmonic equation div |grad u|(p-2). grad u = mu, where mu is a bounded Radon measure. We determine a range of p's for which solutions to the equation verify an a priori estimate. For such p's we also prove a higher integrability result.
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.