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Volume 24, Issue 4
Local Aronson-Bénilan Estimates for Porous Medium Equations Under Ricci Flow

Xiaobao Zhu

DOI: 10.4208/jpde.v24.n4.4

J. Part. Diff. Eq., 24 (2011), pp. 324-333.

Published online: 2011-11

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  • Abstract

In this work we derive local gradient estimates of the Aronson-Bénilan type for positive solutions of porous medium equations under Ricci flow with bounded Ricci curvature. As an application, we derive a Harnack type inequality.

  • Keywords

Aronson-Bénilan estimate Porous medium equation Ricci flow Harnack inequality

  • AMS Subject Headings

35B45 35B53 35K55 35K65 58J35

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{JPDE-24-324, author = {Xiaobao Zhu }, title = {Local Aronson-Bénilan Estimates for Porous Medium Equations Under Ricci Flow}, journal = {Journal of Partial Differential Equations}, year = {2011}, volume = {24}, number = {4}, pages = {324--333}, abstract = {

In this work we derive local gradient estimates of the Aronson-Bénilan type for positive solutions of porous medium equations under Ricci flow with bounded Ricci curvature. As an application, we derive a Harnack type inequality.

}, issn = {2079-732X}, doi = {https://doi.org/10.4208/jpde.v24.n4.4}, url = {http://global-sci.org/intro/article_detail/jpde/5214.html} }
TY - JOUR T1 - Local Aronson-Bénilan Estimates for Porous Medium Equations Under Ricci Flow AU - Xiaobao Zhu JO - Journal of Partial Differential Equations VL - 4 SP - 324 EP - 333 PY - 2011 DA - 2011/11 SN - 24 DO - http://doi.org/10.4208/jpde.v24.n4.4 UR - https://global-sci.org/intro/article_detail/jpde/5214.html KW - Aronson-Bénilan estimate KW - Porous medium equation KW - Ricci flow KW - Harnack inequality AB -

In this work we derive local gradient estimates of the Aronson-Bénilan type for positive solutions of porous medium equations under Ricci flow with bounded Ricci curvature. As an application, we derive a Harnack type inequality.

Xiaobao Zhu . (2011). Local Aronson-Bénilan Estimates for Porous Medium Equations Under Ricci Flow. Journal of Partial Differential Equations. 24 (4). 324-333. doi:10.4208/jpde.v24.n4.4
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