id	author	title	date	pages	extension	mime	words	sentence	flesch	summary	cache	txt
ejde-337	Bieske, Thomas; Blackwell, Keller	Generalizations of the drift Laplace equation in the Heisenberg group and Grushin-type spaces	2021	13	.pdf	application/pdf	4710	315	84	We begin with R3 using the coordinates (x1, x2, x3) and consider the linearly independent vector fields {X1, X2, X3}, defined by: X1 = ∂ ∂x1 − x2 2 ∂ ∂x3 , X2 = ∂ ∂x2 + x1 2 ∂ ∂x3 , X3 = ∂ ∂x3 which obey the relation [X1, X2] = X3. − a)3n(y2 − b) (α+ β − 1)gα+β−2hα+β−2 (4.7) and 2∑ i=1 Yi‖∇0f‖2(Yif) = 4c3(n+ 1)3(α2 + β2)(y1 − a)3n−1g2α+β−3hα+2β−3 × ( (αh+ βg) ( ngh+ c2(n+ 1)(α+ β − 1)(y1 − a)2n+2 ) + ic(n+ 1)2(y1 − a)n+1(y2 − b)(α+ β − 1)(αh− βg) ) , ‖∇0f‖2(Y1Y1f + Y2Y2f)	cache/ejde-337.pdf	txt/ejde-337.txt