Recently, amount of work about the A-harmonic equation for the differential forms has been done. In fact, the A-harmonic equation is an important generalization of the p-harmonic equation in R, p > 1, and the p-harmonic equation is a natural extension of the usual Laplace equation see 1 for the details . The reverse Hölder inequalities have been widely studied and frequently used in analysis an...

We prove the local Hölder continuity of strong local minimizers of the stored energy functional E(u) = ∫ Ω λ|∇u|2 + h(det∇u) dx subject to a condition of ‘positive twist’. The latter turns out to be equivalent to requiring that u maps circles to suitably star-shaped sets. The convex function h(s) grows logarithmically as s → 0+, linearly as s → +∞, and satisfies h(s) = +∞ if s ≤ 0. These proper...

Abstract. In this note, we present two arguments showing that the classical linear adjoint cone restriction conjecture holds for the class of functions supported on the cone and invariant under the spatial rotation in all dimensions. The first is based on a dyadic restriction estimate, while the second follows from a strengthening version of the Hausdorff-Young inequality and the Hölder inequal...

We describe and analyse Levenberg–Marquardt methods for solving systems of nonlinear equations. More specifically, we first propose an adaptive formula for the Levenberg–Marquardt parameter and analyse the local convergence of the method under Hölder metric subregularity. We then introduce a bounded version of the Levenberg–Marquardt parameter and analyse the local convergence of the modified m...

Abstract In this paper, we obtain new Hermite–Hadamard-type inequalities for r -convex and geometrically convex functions and, additionally, some by using the Hölder–İşcan integral inequality an improved power-mean inequality.