Existence of an extremal function of Sobolev critical embedding with an $α$-homogeneous weight
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arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866914951026704384 |
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| author | Gurka, Petr Hauer, Daniel |
| author_facet | Gurka, Petr Hauer, Daniel |
| contents | In our previous publication [{\em Calc. Var. Partial Differential Equations}, 60(1):Paper No. 16, 27, 2021], we delved into examining a critical Sobolev-type embedding of a Sobolev weighted space into an exponential weighted Orlicz space. We specifically determined the optimal Moser-type constant for this embedding, utilizing the monomial weight introduced by Cabré and Ros-Oton [{\em J. Differential Equations}, 255(11):4312--4336, 2013]. Towards the conclusion of that paper, we pledged to explore the existence of an extremal function within this framework.
In this current work, we not only provide a positive affirmation to this inquiry but extend it to a broader range of weights known as \emph{$α$-homogeneous weights}. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2409_11193 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Existence of an extremal function of Sobolev critical embedding with an $α$-homogeneous weight Gurka, Petr Hauer, Daniel Analysis of PDEs 46E35, 46E30, 35A23, 26D10 In our previous publication [{\em Calc. Var. Partial Differential Equations}, 60(1):Paper No. 16, 27, 2021], we delved into examining a critical Sobolev-type embedding of a Sobolev weighted space into an exponential weighted Orlicz space. We specifically determined the optimal Moser-type constant for this embedding, utilizing the monomial weight introduced by Cabré and Ros-Oton [{\em J. Differential Equations}, 255(11):4312--4336, 2013]. Towards the conclusion of that paper, we pledged to explore the existence of an extremal function within this framework. In this current work, we not only provide a positive affirmation to this inquiry but extend it to a broader range of weights known as \emph{$α$-homogeneous weights}. |
| title | Existence of an extremal function of Sobolev critical embedding with an $α$-homogeneous weight |
| topic | Analysis of PDEs 46E35, 46E30, 35A23, 26D10 |
| url | https://arxiv.org/abs/2409.11193 |