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| Format: | Preprint |
| Published: |
2021
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2105.04058 |
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| _version_ | 1866911761115906048 |
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| author | Harrabi, Abdellaziz |
| author_facet | Harrabi, Abdellaziz |
| contents | We investigate {\bf explicit} universal estimate of finite Morse index solutions to polyharmonic equations. \,Differently to previous works \cite{BL2, DDF, fa, H1}, propose here a direct proof using a new interpolation inequality and a delicate boot-strap argument under large superlinear and subcritical growth conditions to show that the universal constant grows as a power function of the Morse index.\, Also, our interpolation inequality allows us to provide local $L^p$-$W^{2r,p}$ estimate. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2105_04058 |
| institution | arXiv |
| publishDate | 2021 |
| record_format | arxiv |
| spellingShingle | Interpolation inequality and some applications Harrabi, Abdellaziz Analysis of PDEs 35G20 (Primary) 35B05 (Secondary) F.2.2; I.2.7 We investigate {\bf explicit} universal estimate of finite Morse index solutions to polyharmonic equations. \,Differently to previous works \cite{BL2, DDF, fa, H1}, propose here a direct proof using a new interpolation inequality and a delicate boot-strap argument under large superlinear and subcritical growth conditions to show that the universal constant grows as a power function of the Morse index.\, Also, our interpolation inequality allows us to provide local $L^p$-$W^{2r,p}$ estimate. |
| title | Interpolation inequality and some applications |
| topic | Analysis of PDEs 35G20 (Primary) 35B05 (Secondary) F.2.2; I.2.7 |
| url | https://arxiv.org/abs/2105.04058 |