Explicit estimates for solutions to higher order elliptic PDEs via Morse index

preprint2015arXivOpen access

In this paper, we establish $L^{\infty}$ and $L^{p}$ estimates for solutions of some polyharmonic elliptic equations via the Morse index. As far as we know, it seems to be the first time that such explicit estimates are obtained for polyharmonic problems.

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Explicit estimates for solutions to higher order elliptic PDEs via Morse index

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