极大次椭圆边值问题的高阶高斯界
Higher-order Gaussian bounds for maximally subelliptic boundary value problems
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中文总结 AI 辅助
该研究针对带边界流形上的扇形极大次椭圆二次型相关热半群，建立了高阶高斯上界，适用于任意偶阶算子、非对称二次型及非狄利克雷边界条件，获热核混合导数的点态界。
中文摘要 AI 辅助
我们建立了带边界流形上一大类扇形极大次椭圆二次型相关热半群的高阶高斯上界。在非特征边界点附近及内部，我们得到了热核关于时间及Hörmander向量场的所有混合导数的点态界，这些界以相关的Carnot–Carathéodory几何形式表达。该结果适用于任意偶阶算子、方程组、非对称二次型及狄利克雷情形之外的边界条件。
英文摘要
We establish higher-order Gaussian upper bounds for the heat semigroups associated with a broad class of sectorial maximally subelliptic quadratic forms on manifolds with boundary. Near non-characteristic boundary points and in the interior, we obtain pointwise bounds for all mixed derivatives of the heat kernel in time and along the Hörmander vector fields, expressed in the associated Carnot--Carathéodory geometry. The results apply to operators of arbitrary even order, systems, nonsymmetric forms, and boundary conditions beyond the Dirichlet case.
