I have seen some regularity result for ellptic PDE but all of them consist of uniform elliptic one. For instance, $$\nabla \cdot (\gamma(x) \nabla u)=F \text{ in } \Omega\qquad u=\phi \text{ on }\partial \Omega$$ with $0<\lambda\le \gamma(x)\le \Lambda<\infty$. Regularity result I am interested are $$\|u\|_{2,\Omega}^2\le C(\|F\|_{0,\Omega}+\|\phi\|_{1/2,\partial\Omega})$$ Is there any result available if we have condition $\gamma(x)\ge 0$?
Any hint or reference will be greatly appreciated.
