an:06666156
Zbl 1352.35215
Feng, X.
Regularity in Orlicz spaces for non-divergence degenerate elliptic equations on homogeneous groups
EN
J. Contemp. Math. Anal., Armen. Acad. Sci. 51, No. 3, 111-120 (2016) and Izv. Nats. Akad. Nauk Armen., Mat. 51, No. 3, 41-55 (2016).
00358502
2016
j
35R03 35B65 35J70
Orlicz estimate; homogeneous group; non-divergence degenerate elliptic equation
Summary: Let \(G\) be a homogeneous group, and let \(X_1,X_2,\cdots,X_{p_0}\) be left-invariant real vector fields on \(G\) that are homogeneous of degree one with respect to the dilation group of \(G\) and satisfy H??rmander's condition. We establish a regularity result in the Orlicz spaces for the following equation:
\[
Lu(x) = \sum\limits_{j = 1}^{{p_0}} {{a_{ij}}(x){X_i}{X_J}u(x)} = f(x),
\]
where \(a_{ij}(x)\) are real valued, bounded measurable functions defined on \(G\), satisfying the uniform ellipticity condition, and belonging to the space \(VMO(G)\) with respect to the subelliptic metric induced by the vector fields \(X_1,X_2,\cdots,X_{p_0}\).