An Application of the Duality Method to the Regularity of Membrane Problems with Friction

Duality is applied to study the regularity of solutions to membrane problems with friction. The method consists of the characterization of the regularity of the subdifferentials of the friction functional. Then the regularity of a solution reduces to the regularity of a solution to a related elliptic boundary value problem or to that of an obstacle problem without friction.     

Everywhere Regularity for Weak Solutions to Variational Inequalities of Triangular Form

In this paper, we obtain two results of weak solutions to variational inequalities of triangular form under controllable growth and a class of natural growth conditions, i.e. 1^°. L^p-estimate for the gradient; 2^°. C^{1,β}_{loc}(Ω, R^N) regularity.     

Regularity Criteria of the Solutions to Axisymmetric Magnetohydrodynamic System

In this paper, we consider Cauchy problem of the axially symmetric Magnetohydrodynamic (MHD) system. By using energy method, we establish some regularity criteria of the solutions for the axisymmetric solutions of the three dimensional incompressible MHD system.     

Regularity Criteria to the Axially Symmetric Tropical Climate Model without Swirl

In this paper, we consider the Cauchy problem of the axially symmetric tropical climate model with fractional dissipation. By using the energy method, we establish a new regularity criteria for the axisymmetric solutions of the 3D Tropical climate model without swirl.