$L^p-L^q$ estimates for non-local heat and wave type equations on locally compact groups
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| Format: | Preprint |
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2024
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| _version_ | 1866917655383900160 |
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| author | Cobos, Santiago Gómez Restrepo, Joel E. Ruzhansky, Michael |
| author_facet | Cobos, Santiago Gómez Restrepo, Joel E. Ruzhansky, Michael |
| contents | We prove the $L^p-L^q$ $(1<p\leqslant 2\leqslant q<+\infty)$ norm estimates for the solutions of heat and wave type equations on a locally compact separable unimodular group $G$ by using an integro-differential operator in time and any positive left invariant operator (maybe unbounded) on $G$. We complement our studies by giving asymptotic time estimates for the solutions, which in some cases are sharp. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2405_00731 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | $L^p-L^q$ estimates for non-local heat and wave type equations on locally compact groups Cobos, Santiago Gómez Restrepo, Joel E. Ruzhansky, Michael Analysis of PDEs 43A15, 43A85, 45K05 We prove the $L^p-L^q$ $(1<p\leqslant 2\leqslant q<+\infty)$ norm estimates for the solutions of heat and wave type equations on a locally compact separable unimodular group $G$ by using an integro-differential operator in time and any positive left invariant operator (maybe unbounded) on $G$. We complement our studies by giving asymptotic time estimates for the solutions, which in some cases are sharp. |
| title | $L^p-L^q$ estimates for non-local heat and wave type equations on locally compact groups |
| topic | Analysis of PDEs 43A15, 43A85, 45K05 |
| url | https://arxiv.org/abs/2405.00731 |