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Regularity of solutions to the polyharmonic equation in general domains |
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| Authors: | Svitlana Mayboroda Vladimir Maz’ya |
| Affiliation: | 1. School of Mathematics, University of Minnesota, 127 Vincent Hall, 206 Church St SE, Minneapolis, MN, 55408, USA 2. Department of Mathematical Sciences, M&O Building, University of Liverpool, Liverpool, L69 3BX, UK 3. Department of Mathematics, Link?ping University, 581 83, Link?ping, Sweden |
| Abstract: | The present paper establishes boundedness of $[m-frac{n}{2}+frac{1}{2} ]$ derivatives for the solutions to the polyharmonic equation of order 2m in arbitrary bounded open sets of ${mathbb{R}}^{n}$ , 2≤n≤2m+1, without any restrictions on the geometry of the underlying domain. It is shown that this result is sharp and cannot be improved in general domains. Moreover, it is accompanied by sharp estimates on the polyharmonic Green function. |
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