Everywhere Hölder Continuity of Solutions of Certain Degenerate Elliptic Systems

Continuity Properties of Solutions to Some Degenerate Elliptic Equations

We consider a nonlinear (possibly) degenerate elliptic operator Lv = − div a(∇v) + b(x, v) where the functions a and b are, unnecessarly strictly, monotonic. For a given boundary datum φ we prove the existence of the maximum and the minimum of the solutions and formulate a Haar-Rado type result, namely a continuity property for these solutions that may follow from the continuity of φ. In the ho...

Erratum: On the Hölder Continuity of Solutions of a Certain System Related to Maxwell's Equations

We study the system curl (a(x) curlu) = 0, divu = 0 with a bounded measurable coefficient a(x). The main result of this paper is the Hölder continuity of weak solutions of the system above. As an application, we prove the Cα regularity of weak solutions of the Maxwell’s equations in a quasi-stationary electromagnetic field.

The Hölder continuity of solutions to generalized vector equilibrium problems

In this paper, by using a weaker assumption, we discuss the Hölder continuity of solution maps for two cases of parametric generalized vector equilibrium problems under the case that the solution map is a general set-valued one, but not a single-valued one. These results extend the recent ones in the literature. Several examples are given for the illustration of our results.

Hölder continuity of a parametric variational inequality

‎In this paper‎, ‎we study the Hölder continuity of solution mapping to a parametric variational inequality‎. ‎At first‎, ‎recalling a real-valued gap function of the problem‎, ‎we discuss the Lipschitz continuity of the gap function‎. ‎Then under the strong monotonicity‎, ‎we establish the Hölder continuity of the single-valued solution mapping for the problem‎. ‎Finally‎, ‎we apply these resu...

On the Spectral Properties of Degenerate Non-selfadjoint Elliptic systems of Differential Operators