与Hörmander矢量场相关的有界系数散度退化椭圆方程的一个De Giorgi型结果

Pub Date : 2023-01-01 DOI:10.4208/jpde.v36.n1.2

Lingling Hou

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引用次数: 0

摘要

．本文研究了由H¨ormander向量场构造的带有界系数的散度退化椭圆方程。我们通过提供一个De Giorgi型引理并将Moser迭代推广到这里的集合，证明了方程弱解的一个De Giorgi型结果，即局部H¨old连续性。同时给出了弱解的哈纳克不等式

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A De Giorgi Type Result to Divergence Degenerate Elliptic Equation with Bounded Coefficients Related To Hörmander's Vector Fields

. In this paper, we consider the divergence degenerate elliptic equation with bounded coefﬁcients constructed by H¨ormander’s vector ﬁelds. We prove a De Giorgi type result, i.e., the local H¨older continuity for the weak solutions to the equation by providing a De Giorgi type lemma and extending the Moser iteration to the setting here. As a consequence, the Harnack inequality of weak solutions is also given

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