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October 23, 2025Asymptotic Analysis

A Critical Nonlocal Double Phase Problem in the Heisenberg Group With a Modified Hardy Potential

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A critical solution emerged, applying the modified Hardy's inequality to fractional Laplacians.
This research addresses the critical double phase problem and establishes functional outcomes using a Hardy potential.
Observational analysis applied a Carathéodory function in the Heisenberg group to demonstrate solution existence.
Findings emphasize the importance of the modified Hardy's inequality in this mathematical context.

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Implication

This research reveals a solution to the critical double phase problem in the Heisenberg group, indicating significant implications for Hardy inequalities.

Cite This Study

Mukherjee et al. (2025) studied this question.

synapsesocial.com/papers/68f984011881b68f3b7ae4df https://doi.org/10.1177/09217134251386204

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Implication

This research reveals a solution to the critical double phase problem in the Heisenberg group, indicating significant implications for Hardy inequalities.

A Critical Nonlocal Double Phase Problem in the Heisenberg Group With a Modified Hardy Potential

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Discussion

Implication

Cite This Study

A Critical Nonlocal Double Phase Problem in the Heisenberg Group With a Modified Hardy Potential

Key Points

Discussion

Implication

Cite This Study

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Also Consider