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Volume 36, Issue 1
A De Giorgi Type Result to Divergence Degenerate Elliptic Equation with Bounded Coefficients Related to Hörmander's Vector Fields

Lingling Hou

DOI: 10.4208/jpde.v36.n1.2

J. Part. Diff. Eq., 36 (2023), pp. 22-47.

Published online: 2022-12

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  • Abstract

In this paper, we consider the divergence degenerate elliptic equation with bounded coefficients constructed by Hörmander's vector fields. We prove a De Giorgi type result, i.e., the local Hölder 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.

  • Keywords

Divergence degenerate elliptic equation Hörmander's vector fields De Giorgi type result Harnack inequality.

  • AMS Subject Headings

35B45, 35B65, 35D30, 35J70

  • Copyright

COPYRIGHT: © Global Science Press

  • Email address

hll67800@163.com (Lingling Hou)

  • BibTex
  • RIS
  • TXT
@Article{JPDE-36-22, author = {Hou , Lingling}, title = {A De Giorgi Type Result to Divergence Degenerate Elliptic Equation with Bounded Coefficients Related to Hörmander's Vector Fields}, journal = {Journal of Partial Differential Equations}, year = {2022}, volume = {36}, number = {1}, pages = {22--47}, abstract = {

In this paper, we consider the divergence degenerate elliptic equation with bounded coefficients constructed by Hörmander's vector fields. We prove a De Giorgi type result, i.e., the local Hölder 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.

}, issn = {2079-732X}, doi = {https://doi.org/10.4208/jpde.v36.n1.2}, url = {http://global-sci.org/intro/article_detail/jpde/21291.html} }
TY - JOUR T1 - A De Giorgi Type Result to Divergence Degenerate Elliptic Equation with Bounded Coefficients Related to Hörmander's Vector Fields AU - Hou , Lingling JO - Journal of Partial Differential Equations VL - 1 SP - 22 EP - 47 PY - 2022 DA - 2022/12 SN - 36 DO - http://doi.org/10.4208/jpde.v36.n1.2 UR - https://global-sci.org/intro/article_detail/jpde/21291.html KW - Divergence degenerate elliptic equation KW - Hörmander's vector fields KW - De Giorgi type result KW - Harnack inequality. AB -

In this paper, we consider the divergence degenerate elliptic equation with bounded coefficients constructed by Hörmander's vector fields. We prove a De Giorgi type result, i.e., the local Hölder 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.

Hou , Lingling. (2022). A De Giorgi Type Result to Divergence Degenerate Elliptic Equation with Bounded Coefficients Related to Hörmander's Vector Fields. Journal of Partial Differential Equations. 36 (1). 22-47. doi:10.4208/jpde.v36.n1.2
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