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arXiv · 2401.15274

Weighted Trudinger-Moser inequalities in the subcritical Sobolev spaces and their applications

Masahiro Ikeda·Megumi Sano·Koichi Taniguchi
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Abstract

We study boundedness, optimality and attainability of Trudinger-Moser type maximization problems in the radial and the subcritical homogeneous Sobolev spaces $\dot{W}^{1,p}_{0, \text{rad}}(B_R^N)\,(p<N)$. Our results give a revision of an error in \cite[Theorem C]{HL}. Also, our inequality converges to the original Trudinger-Moser inequality as $p \nearrow N$ including optimal exponent and concentration limit. Finally, we consider an application of our inequality to elliptic problems with exponential nonlinearity.

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Masahiro Ikeda, Megumi Sano, Koichi Taniguchi. 2024-01-27. Weighted Trudinger-Moser inequalities in the subcritical Sobolev spaces and their applications. https://arxiv.org/abs/2401.15274

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