Classical solutions for the pressure-gradient equations in non-smooth and non-convex domains

We establish the existence of the classical solution for the pressure-gradient equation in a nonsmooth and non-convex domain. The equation is elliptic inside the domain, becomes degenerate on the boundary, and is singular at the origin when the origin lies on the boundary. We show the solution is smooth inside the domain and continuous up to the boundary.  2004 Elsevier Inc. All rights reserved.