Hölder regularity of solutions to some classes of elliptic systems in convex nonsmooth domains

Abstract

We prove Hölder continuity up to the boundaryof a convex nonsmooth domain of weak solutions to a class of linear second order elliptic systems with discontinuous coefficients under a suitable condition on the dispersion of eigenvalues of the coefficients matrix. The above results are applied to quasilinear and nonlinear systems.

Moreover, the existence and uniqueness of very weak solutions with L_1 right hand sides is proved.

Keywords

• Hölder
• regularity
• solutions
• classes
• elliptic
• systems
• convex
• nonsmooth
• domains