标题： Heisenberg群中次椭圆方程的边界正则性 显示英文标题

标题： Boundary regularity for subelliptic equations in the Heisenberg group

摘要： 我们证明了一类退化椭圆型、二阶、非齐次的非散度形式方程在Heisen堡群左不变向量场结构下的边界Hölder和Lipschitz正则性。 我们的重点是具有有界可测系数以及有界右端项的算子；必要时，我们对方程的椭圆性比值和源项在边界特征点附近的增长率施加维度限制。 对于在特征半空间$\{t>0\}$中的解，当源项属于适当的加权$L^{\infty}$空间时，我们在原点附近得到了一个内在的二阶展开；即使对于经常研究的次拉普拉斯算子，这也是一个新的结果。 显示英文摘要

摘要： We prove boundary H\"older and Lipschitz regularity for a class of degenerate elliptic, second order, inhomogeneous equations in non-divergence form structured on the left-invariant vector fields of the Heisenberg group. Our focus is on the case of operators with bounded and measurable coefficients and bounded right-hand side; when necessary, we impose a dimensional restriction on the ellipticity ratio and a growth rate for the source term near characteristic points of the boundary. For solutions in the characteristic half-space $\{t>0\}$, we obtain an intrinsic second order expansion near the origin when the source term belongs to an appropriate weighted $L^{\infty}$ space; this is a new result even for the frequently studied sub-Laplacian.