Struwe's decomposition for a polyharmonic operator on a compact Riemannian manifold with or without boundary

Saikat Mazumdar

doi:10.3934/cpaa.2017015

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2017, Volume 16, Issue 1: 311-330. Doi: 10.3934/cpaa.2017015

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Struwe's decomposition for a polyharmonic operator on a compact Riemannian manifold with or without boundary

Saikat Mazumdar

Institut Elie Cartan de Lorraine, Université de Lorraine, BP 70239,54506 Vandœuvre-lès-Nancy, France

Author Bio: E-mail address: saikat.mazumdar@univ-lorraine.fr

Received: April 30, 2016

Revised: June 30, 2016

Published: January 2018

This work is part of the PhD thesis of the author, funded by "Fédération Charles Hermite" (FR3198 du CNRS) and "Région Lorraine". The author acknowledges these two institutions for their supports.

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Abstract

Given a high-order elliptic operator on a compact manifold with or without boundary, we perform the decomposition of Palais-Smale sequences for a nonlinear problem as a sum of bubbles. This is a generalization of the celebrated 1984 result of Struwe ^[19]. Unlike the case of second-order operators, bubbles close to the boundary might appear. Our result includes the case of a smooth bounded domain of $\mathbb{R}^{n}$.

Keywords:

Struwe decomposition,
polyharmonic operators on manifolds,
higher order elliptic problems with critical Sobolev growth.

Mathematics Subject Classification: 35J35, 58J60.

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References

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