The Orlicz Electrostatic <i>q</i>-Capacity Minkowski Problem
The existence of solutions to the discrete Orlicz electrostatic <i>q</i>-capacity Minkowski problem was given by Ji and Yang when <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mn>1<...
Saved in:
| Main Authors: | , , , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
MDPI AG
2025-01-01
|
| Series: | Axioms |
| Subjects: | |
| Online Access: | https://www.mdpi.com/2075-1680/14/2/86 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1850082231880515584 |
|---|---|
| author | Hui Zeng Lijuan Liu Lu Yin Rigao He |
| author_facet | Hui Zeng Lijuan Liu Lu Yin Rigao He |
| author_sort | Hui Zeng |
| collection | DOAJ |
| description | The existence of solutions to the discrete Orlicz electrostatic <i>q</i>-capacity Minkowski problem was given by Ji and Yang when <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mn>1</mn><mo><</mo><mi>p</mi><mo><</mo><mn>2</mn></mrow></semantics></math></inline-formula>. Now, we have studied the problem by removing the assumption that the measure <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>μ</mi></semantics></math></inline-formula> does not have a pair of antipodal point masses. By means of approximation, the sufficient condition is given for the existence of solutions to this problem for general measures when <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mn>1</mn><mo><</mo><mi>q</mi><mo><</mo><mn>2</mn></mrow></semantics></math></inline-formula>, which is an extension of the <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi>L</mi><mi>p</mi></msub></semantics></math></inline-formula> electrostatic <i>q</i>-capacity Minkowski problem when <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mn>1</mn><mo><</mo><mi>q</mi><mo><</mo><mn>2</mn></mrow></semantics></math></inline-formula>. |
| format | Article |
| id | doaj-art-d2d4b35c3de242e097fd9dc79e5be1d3 |
| institution | DOAJ |
| issn | 2075-1680 |
| language | English |
| publishDate | 2025-01-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Axioms |
| spelling | doaj-art-d2d4b35c3de242e097fd9dc79e5be1d32025-08-20T02:44:34ZengMDPI AGAxioms2075-16802025-01-011428610.3390/axioms14020086The Orlicz Electrostatic <i>q</i>-Capacity Minkowski ProblemHui Zeng0Lijuan Liu1Lu Yin2Rigao He3School of Mathematics and Statistics, Hunan University of Science and Technology, Xiangtan 411201, ChinaSchool of Mathematics and Statistics, Hunan University of Science and Technology, Xiangtan 411201, ChinaSchool of Mathematics and Statistics, Hunan University of Science and Technology, Xiangtan 411201, ChinaDepartment of Mathematics, Jiangxi University of Science and Technology, Ganzhou 341000, ChinaThe existence of solutions to the discrete Orlicz electrostatic <i>q</i>-capacity Minkowski problem was given by Ji and Yang when <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mn>1</mn><mo><</mo><mi>p</mi><mo><</mo><mn>2</mn></mrow></semantics></math></inline-formula>. Now, we have studied the problem by removing the assumption that the measure <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>μ</mi></semantics></math></inline-formula> does not have a pair of antipodal point masses. By means of approximation, the sufficient condition is given for the existence of solutions to this problem for general measures when <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mn>1</mn><mo><</mo><mi>q</mi><mo><</mo><mn>2</mn></mrow></semantics></math></inline-formula>, which is an extension of the <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi>L</mi><mi>p</mi></msub></semantics></math></inline-formula> electrostatic <i>q</i>-capacity Minkowski problem when <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mn>1</mn><mo><</mo><mi>q</mi><mo><</mo><mn>2</mn></mrow></semantics></math></inline-formula>.https://www.mdpi.com/2075-1680/14/2/86Orlicz–Minkowski problemelectrostatic <i>q</i>-capacityOrlicz electrostatic <i>q</i>-capacitary measure |
| spellingShingle | Hui Zeng Lijuan Liu Lu Yin Rigao He The Orlicz Electrostatic <i>q</i>-Capacity Minkowski Problem Axioms Orlicz–Minkowski problem electrostatic <i>q</i>-capacity Orlicz electrostatic <i>q</i>-capacitary measure |
| title | The Orlicz Electrostatic <i>q</i>-Capacity Minkowski Problem |
| title_full | The Orlicz Electrostatic <i>q</i>-Capacity Minkowski Problem |
| title_fullStr | The Orlicz Electrostatic <i>q</i>-Capacity Minkowski Problem |
| title_full_unstemmed | The Orlicz Electrostatic <i>q</i>-Capacity Minkowski Problem |
| title_short | The Orlicz Electrostatic <i>q</i>-Capacity Minkowski Problem |
| title_sort | orlicz electrostatic i q i capacity minkowski problem |
| topic | Orlicz–Minkowski problem electrostatic <i>q</i>-capacity Orlicz electrostatic <i>q</i>-capacitary measure |
| url | https://www.mdpi.com/2075-1680/14/2/86 |
| work_keys_str_mv | AT huizeng theorliczelectrostaticiqicapacityminkowskiproblem AT lijuanliu theorliczelectrostaticiqicapacityminkowskiproblem AT luyin theorliczelectrostaticiqicapacityminkowskiproblem AT rigaohe theorliczelectrostaticiqicapacityminkowskiproblem AT huizeng orliczelectrostaticiqicapacityminkowskiproblem AT lijuanliu orliczelectrostaticiqicapacityminkowskiproblem AT luyin orliczelectrostaticiqicapacityminkowskiproblem AT rigaohe orliczelectrostaticiqicapacityminkowskiproblem |