一类p-次双权退化椭圆算子及其边值问题的唯一性

A direct uniqueness proof for equations related to a class of degenerated elliptics operators with a double-weight

通过对广义Baouendi-Grushin算子L=△x+|x|2α△y(α>0,x∈Rn,y∈Rm)的向量场分别加权,提出一类失去反自共轭性双权退化向量场.通过讨论泛函的严格凸性,在有界单连通区域内,给出p次退化椭圆算子的第一特征值的单一性.

In this paper, by adding respective double-weight to the vector field for generalized Baouendi-Grushin operator L = △x ＋｜x｜^2α△y（α〉0,x∈R^n,y∈ R^m）, we propose a kind of loses counter-from the conjugational double-weight degeneration vector field. After functional is strict through the discussion of convexity, we produce the first characteristic value simplicity for p time of degenerated ellipse operator in a bounded simply connected domain.