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

Published 16 Nov 2015 in math.AP | (1511.04907v1)

Abstract: 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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