On the Robin problems of degenerate elliptic equations

Abstract

Let Ω be a bounded smooth domain in $R^N(N\ge 3)$ with $0\in \Omega$. Positive weak solutions of the Robin problems of a class of degenerate elliptic equations are obtained via variational methods and new embeddings related to new Caffarelli-Kohn-Nirenberg inequalities. Meanwhile, the further regularities of the weak solutions are studied, especially, the regularities at the singular point $x=0$ of the solutions are obtained.