On functionals involving the $p$-capacity and the $q$-torsional rigidity
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866916859877523456 |
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| author | Berg, Michiel van den Gavitone, Nunzia |
| author_facet | Berg, Michiel van den Gavitone, Nunzia |
| contents | Upper bounds are obtained for the $p$-capacity of compact sets in $\R^d$, with $d \ge 2$ and $1<p<d$. Upper and lower bounds are obtained for the product of $p$-capacity and powers of the $q$-torsional rigidity over the collection of all non-empty, open, bounded and convex sets in $\R^d$ with either a perimeter constraint, or a measure constraint, or a combination of perimeter and measure constraints. For some range of parameters we identify the ball as the unique (up to homotheties) maximiser or minimiser respectively. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2412_06563 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On functionals involving the $p$-capacity and the $q$-torsional rigidity Berg, Michiel van den Gavitone, Nunzia Analysis of PDEs 49Q10, 49J45, 49J40, 35J25 Upper bounds are obtained for the $p$-capacity of compact sets in $\R^d$, with $d \ge 2$ and $1<p<d$. Upper and lower bounds are obtained for the product of $p$-capacity and powers of the $q$-torsional rigidity over the collection of all non-empty, open, bounded and convex sets in $\R^d$ with either a perimeter constraint, or a measure constraint, or a combination of perimeter and measure constraints. For some range of parameters we identify the ball as the unique (up to homotheties) maximiser or minimiser respectively. |
| title | On functionals involving the $p$-capacity and the $q$-torsional rigidity |
| topic | Analysis of PDEs 49Q10, 49J45, 49J40, 35J25 |
| url | https://arxiv.org/abs/2412.06563 |