应用泛函分析学报
應用汎函分析學報
응용범함분석학보
ACTA ANALYSIS FUNCTIONALIS APPLICATA
2009年
4期
314-317
,共4页
退化椭圆方程%Kato类%Green函数
退化橢圓方程%Kato類%Green函數
퇴화타원방정%Kato류%Green함수
degenerate elliptic equation%Kato class%Green function
在区域Ω上考虑一类由退化向量场形成的Schrodinger方程∑_(i=1)~mX_1~*(a_(ij)(x)X_ju)-νu=0)其中X_1,…,X_m为R~n(n≥3)上满足Hormander条件的实C~∞向量场,X_i~*为X_i的形式共轭,v属于Kato类的某一类比K_η~(loc)(Ω).并得到以下结果:若"为以上方程的弱解,则｜Xu｜~2w=∑_(i=1)~m｜X_i,u｜~2w∈K_η~(loc)(Ω).
在區域Ω上攷慮一類由退化嚮量場形成的Schrodinger方程∑_(i=1)~mX_1~*(a_(ij)(x)X_ju)-νu=0)其中X_1,…,X_m為R~n(n≥3)上滿足Hormander條件的實C~∞嚮量場,X_i~*為X_i的形式共軛,v屬于Kato類的某一類比K_η~(loc)(Ω).併得到以下結果:若"為以上方程的弱解,則｜Xu｜~2w=∑_(i=1)~m｜X_i,u｜~2w∈K_η~(loc)(Ω).
재구역Ω상고필일류유퇴화향량장형성적Schrodinger방정∑_(i=1)~mX_1~*(a_(ij)(x)X_ju)-νu=0)기중X_1,…,X_m위R~n(n≥3)상만족Hormander조건적실C~∞향량장,X_i~*위X_i적형식공액,v속우Kato류적모일류비K_η~(loc)(Ω).병득도이하결과:약"위이상방정적약해,칙｜Xu｜~2w=∑_(i=1)~m｜X_i,u｜~2w∈K_η~(loc)(Ω).
We considered the weak solution of a class of Schrodinger equation formed by degenerated vector field∑_(i=1)~mX_1~*(a_(ij)(x)X_ju)-νu=0)where X_1,…,X_m are C~∞ vector fields on R~n (n≥3) satisfying Hormander condition, X_t~* is the formal adjoint of X_t. v belongs to some analogue of the kato-stummel class K_η~(loc)(Ω). We obtain the following result: let u be a weak solution of the equation ∑_(i=1)~mX_1~*(a_(ij)(x)X_ju)-νu=0),then ｜Xu｜~2w=∑_(i=1)~m｜X_i,u｜~2w∈K_η~(loc)(Ω).
