The objective of this work is to bring the positive answer presented by Bonatti and Franks to the question proposed by Wilkinson about the existence or not of a continuous non-singular vector field of $\mathbb{R}^2$ tangent ...

We prove sharp Holder continuity and an estimate of rupture sets for sequences of solutions of the following nonlinear problem with negative exponent Delta u =1/u(p) in Omega, p > 1. As a consequence, we prove the ...

We present new sufficient convergence conditions for the semilocal convergence of Newton’s method to a locally unique solution of a nonlinear equation in a Banach space. We use Hölder and center Hölder conditions, instead ...

The Chalker-Coddington quantum network percolation model is numerically pertinent to the understanding of the delocalization transition of the quantum Hall effect. We study the model restricted to a cylinder of perimeter ...

We obtain a Harnack type inequality for solutions to elliptic equations in divergence form with non-standard p(x)-type growth. A model equation is the inhomogeneous p(x)-Laplacian. Namely, ∆p(x)u := div |∇u| p(x)−2∇u = ...