Existence and uniqueness are proved by Lax-Milgram theorem for a type of degenerate divergence elliptic equation in a type of Sobolev spaces with weight, and also the regularity will be studied.

• 先用Lax-Milgram定理证明一类退化散度型椭圆型方程在带权Sobolev空间中弱解的存在唯一性,然后证明解的正则性。