Lorentz estimates for asymptotically regular elliptic equations in quasiconvex domains

Abstract

We derive a global Lorentz estimate of the gradient of weak solutions to nonlinear elliptic problems with asymptotically regular nonlinearity in quasiconvex domains. Here, we prove its Lorentz estimate for such an asymptotically regular elliptic problem by constructing a regular problem via Poisson's formula, and quasiconvex domain locally approximated by convex domain.

Keywords

• Lorentz estimate
• Poisson kernel
• Lorentz space
• regularity