We construct examples, that log Hölder continuity of the integrated density of states cannot be improved. Our examples are limit-periodic.

We consider a class of inverse problems defined by a nonlinear mapping from parameter or model functions to the data, where the inverse mapping is Hölder continuous with respect to appropriate Banach spaces. We analyze a nonlinear Landweber iteration and prove local convergence and convergence rates with respect to an appropriate distance measure. Opposed to the standard analysis of the nonline...

We study partial regularity of very weak solutions to some nonhomogeneous A-harmonic systems. To obtain the reverse Hölder inequality of the gradient of a very weak solution, we construct a suitable test function by Hodge decomposition. With the aid of Gehring's lemma, we prove that these very weak solutions are weak solutions. Further, we show that these solutions are in fact optimal Hölder co...

In dimension three, we establish the existence of weak solutions {u,H,E} to the Landau-Lifshitz equation (1.1) coupled with the time-dependent Maxwell equation (1.2)-(1.3) such that u is Hölder continuous away from a closed set Σ, which has locally finite 3-dimensional parabolic Hausdorff measure. For two reduced Maxwell equations (1.17) and (1.18), Hölder continuity of ∇u away from Σ is also e...

In this paper we present the methods of Quasilinearization and Generalized Quasilinearization for hybrid Caputo fractional differential equations which are Caputo fractional differential equations with fixed moments of impulse. In order to prove this results we use the weakened assumption of -continuity in place of local Hölder continuity.

We study regularity properties of weak solutions to elliptic equations involving variable growth exponents. We prove the sufficiency of a Wiener type criterion for the regularity of boundary points. This criterion is formulated in terms of the natural capacity involving the variable growth exponent. We also prove the Hölder continuity of weak solutions up to the boundary in domains with uniform...

In this paper, we study the semilocal convergence of a fifth order iterative method using recurrence relation under the assumption that first order Fréchet derivative satisfies the Hölder condition. Also, we calculate the R-order of convergence and provide some a priori error bounds. Based on this, we give existence and uniqueness region of the solution for a nonlinear Hammerstein integral equa...