Year: 2020
Author: Junli Zhang, Pengcheng Niu, Xiuxiu Wang
Journal of Mathematical Study, Vol. 53 (2020), Iss. 3 : pp. 265–296
Abstract
In this paper, we concern the divergence Kohn-Laplace equation
$$\sum\limits_{i = 1}^n {\sum\limits_{j = 1}^n {\left( {X_j^*({a^{ij}}{X_i}u) + Y_j^*({b^{ij}}{Y_i}u)} \right)} } + Tu = f - \sum\limits_{i = 1}^n {\left( {X_i^*{f^i} + Y_i^*{g^i}} \right)}$$ with bounded coefficients on the Heisenberg group ${{\mathbb{H}}^n}$, where ${X_1}, \cdots, {X_n},{Y_1}, \cdots, {Y_n}$ and $T$ are real smooth vector fields defined in a bounded region $\Omega \subset {\mathbb{H}^n}$. The local maximum principle of weak solutions to the equation is established. The oscillation properties of the weak solutions are studied and then the Hölder regularity and weak Harnack inequality of the weak solutions are proved.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/jms.v53n3.20.03
Journal of Mathematical Study, Vol. 53 (2020), Iss. 3 : pp. 265–296
Published online: 2020-01
AMS Subject Headings:
Copyright: COPYRIGHT: © Global Science Press
Pages: 32
Keywords: Heisenberg group Kohn-Laplace equation local maximum principle Hölder regularity weak Harnack inequality.