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Gradient estimate of equations with potential under the almost Ricci soliton condition | ||
| International Journal of Nonlinear Analysis and Applications | ||
| مقالات آماده انتشار، اصلاح شده برای چاپ، انتشار آنلاین از تاریخ 12 خرداد 1404 اصل مقاله (448.86 K) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.22075/ijnaa.2023.28958.4031 | ||
| نویسندگان | ||
| Sakineh Hajiaghasi* 1؛ Shahroud Azami2 | ||
| 1Department of pure mathematics, Faculty of science, Imam Khomeini International University, Qazvin, Iran | ||
| 2Department of Pure Mathematics, Faculty of Sciences, Imam Khomeini International University, Qazvin, Iran | ||
| تاریخ دریافت: 20 آبان 1401، تاریخ بازنگری: 20 مهر 1402، تاریخ پذیرش: 01 دی 1402 | ||
| چکیده | ||
| Using volume comparison theorems and the Sobolev inequality with almost Ricci solitons, we study an important version of the gradient estimate for the solutions of $\Delta u=f+Hu$, for some function $f$, $H$, and we obtain an upper bound for the gradient of $u$ on almost Ricci solitons. | ||
| کلیدواژهها | ||
| Sobolev constant؛ Gradient estimate؛ Ricci soliton؛ Bakry-{\'E}mery Ricci curvature | ||
| مراجع | ||
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