A priori estimates of solutions to nonlinear fractional Laplacian equation
In this paper, we focus on the research of a priori estimates of several types of semi-linear fractional Laplacian equations with a critical Sobolev exponent. Employing the method of moving planes, we can achieve a priori estimates which are closely connected to the existence of solutions to nonline...
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| Format: | Article |
| Language: | English |
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AIMS Press
2023-01-01
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| Series: | Electronic Research Archive |
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| Online Access: | https://www.aimspress.com/article/doi/10.3934/era.2023056?viewType=HTML |
| _version_ | 1827954287483813888 |
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| author | Tao Zhang Tingzhi Cheng |
| author_facet | Tao Zhang Tingzhi Cheng |
| author_sort | Tao Zhang |
| collection | DOAJ |
| description | In this paper, we focus on the research of a priori estimates of several types of semi-linear fractional Laplacian equations with a critical Sobolev exponent. Employing the method of moving planes, we can achieve a priori estimates which are closely connected to the existence of solutions to nonlinear fractional Laplacian equations. Our result can extend a priori estimates of the second order elliptic equation to the fractional Laplacian equation and we believe that the method used here will be applicable to more general nonlocal problems. |
| first_indexed | 2024-04-09T14:27:47Z |
| format | Article |
| id | doaj.art-f9ff330459f148ddba551c3fbc44953c |
| institution | Directory Open Access Journal |
| issn | 2688-1594 |
| language | English |
| last_indexed | 2024-04-09T14:27:47Z |
| publishDate | 2023-01-01 |
| publisher | AIMS Press |
| record_format | Article |
| series | Electronic Research Archive |
| spelling | doaj.art-f9ff330459f148ddba551c3fbc44953c2023-05-04T01:20:24ZengAIMS PressElectronic Research Archive2688-15942023-01-013121119113310.3934/era.2023056A priori estimates of solutions to nonlinear fractional Laplacian equationTao Zhang 0Tingzhi Cheng11. School of Mathematics and Information Science, Yantai University, Yantai 264005, China2. School of Mathematics and Statistics Science, Ludong University, Yantai 264025, ChinaIn this paper, we focus on the research of a priori estimates of several types of semi-linear fractional Laplacian equations with a critical Sobolev exponent. Employing the method of moving planes, we can achieve a priori estimates which are closely connected to the existence of solutions to nonlinear fractional Laplacian equations. Our result can extend a priori estimates of the second order elliptic equation to the fractional Laplacian equation and we believe that the method used here will be applicable to more general nonlocal problems.https://www.aimspress.com/article/doi/10.3934/era.2023056?viewType=HTMLa priori estimatesfractional laplaciannonlocal problems |
| spellingShingle | Tao Zhang Tingzhi Cheng A priori estimates of solutions to nonlinear fractional Laplacian equation Electronic Research Archive a priori estimates fractional laplacian nonlocal problems |
| title | A priori estimates of solutions to nonlinear fractional Laplacian equation |
| title_full | A priori estimates of solutions to nonlinear fractional Laplacian equation |
| title_fullStr | A priori estimates of solutions to nonlinear fractional Laplacian equation |
| title_full_unstemmed | A priori estimates of solutions to nonlinear fractional Laplacian equation |
| title_short | A priori estimates of solutions to nonlinear fractional Laplacian equation |
| title_sort | priori estimates of solutions to nonlinear fractional laplacian equation |
| topic | a priori estimates fractional laplacian nonlocal problems |
| url | https://www.aimspress.com/article/doi/10.3934/era.2023056?viewType=HTML |
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