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<...

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Bibliographic Details
Main Authors: Hui Zeng, Lijuan Liu, Lu Yin, Rigao He
Format: Article
Language:English
Published: MDPI AG 2025-01-01
Series:Axioms
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Online Access:https://www.mdpi.com/2075-1680/14/2/86
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Summary: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>.
ISSN:2075-1680