Symmetry and Monotonicity of Solutions to Mixed Local and Nonlocal Weighted Elliptic Equations
This paper focuses on the symmetry and monotonicity of non-negative solutions to a mixed local and nonlocal weighted elliptic problem. This problem generalizes the ground-state representation of elliptic equations with the Hardy potential. The novelty of this research lies in developing the moving p...
Saved in:
| Main Authors: | , , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
MDPI AG
2025-02-01
|
| Series: | Axioms |
| Subjects: | |
| Online Access: | https://www.mdpi.com/2075-1680/14/2/139 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1850081383322484736 |
|---|---|
| author | Yongzhi Daiji Shuibo Huang Qiaoyu Tian |
| author_facet | Yongzhi Daiji Shuibo Huang Qiaoyu Tian |
| author_sort | Yongzhi Daiji |
| collection | DOAJ |
| description | This paper focuses on the symmetry and monotonicity of non-negative solutions to a mixed local and nonlocal weighted elliptic problem. This problem generalizes the ground-state representation of elliptic equations with the Hardy potential. The novelty of this research lies in developing the moving planes method for mixed local and nonlocal equations with a weighted function, thus clarifying the influence of the weighted function on the solution properties. |
| format | Article |
| id | doaj-art-99b873ba47594659963e449bf724f120 |
| institution | DOAJ |
| issn | 2075-1680 |
| language | English |
| publishDate | 2025-02-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Axioms |
| spelling | doaj-art-99b873ba47594659963e449bf724f1202025-08-20T02:44:45ZengMDPI AGAxioms2075-16802025-02-0114213910.3390/axioms14020139Symmetry and Monotonicity of Solutions to Mixed Local and Nonlocal Weighted Elliptic EquationsYongzhi Daiji0Shuibo Huang1Qiaoyu Tian2School of Mathematics and Computer Science, Northwest Minzu University, Lanzhou 730030, ChinaSchool of Mathematics and Computer Science, Northwest Minzu University, Lanzhou 730030, ChinaSchool of Mathematics and Computer Science, Northwest Minzu University, Lanzhou 730030, ChinaThis paper focuses on the symmetry and monotonicity of non-negative solutions to a mixed local and nonlocal weighted elliptic problem. This problem generalizes the ground-state representation of elliptic equations with the Hardy potential. The novelty of this research lies in developing the moving planes method for mixed local and nonlocal equations with a weighted function, thus clarifying the influence of the weighted function on the solution properties.https://www.mdpi.com/2075-1680/14/2/139mixed local and nonlocalsymmetrymonotonicitymoving planes method |
| spellingShingle | Yongzhi Daiji Shuibo Huang Qiaoyu Tian Symmetry and Monotonicity of Solutions to Mixed Local and Nonlocal Weighted Elliptic Equations Axioms mixed local and nonlocal symmetry monotonicity moving planes method |
| title | Symmetry and Monotonicity of Solutions to Mixed Local and Nonlocal Weighted Elliptic Equations |
| title_full | Symmetry and Monotonicity of Solutions to Mixed Local and Nonlocal Weighted Elliptic Equations |
| title_fullStr | Symmetry and Monotonicity of Solutions to Mixed Local and Nonlocal Weighted Elliptic Equations |
| title_full_unstemmed | Symmetry and Monotonicity of Solutions to Mixed Local and Nonlocal Weighted Elliptic Equations |
| title_short | Symmetry and Monotonicity of Solutions to Mixed Local and Nonlocal Weighted Elliptic Equations |
| title_sort | symmetry and monotonicity of solutions to mixed local and nonlocal weighted elliptic equations |
| topic | mixed local and nonlocal symmetry monotonicity moving planes method |
| url | https://www.mdpi.com/2075-1680/14/2/139 |
| work_keys_str_mv | AT yongzhidaiji symmetryandmonotonicityofsolutionstomixedlocalandnonlocalweightedellipticequations AT shuibohuang symmetryandmonotonicityofsolutionstomixedlocalandnonlocalweightedellipticequations AT qiaoyutian symmetryandmonotonicityofsolutionstomixedlocalandnonlocalweightedellipticequations |