# American Institute of Mathematical Sciences

January  2017, 16(1): 311-330. doi: 10.3934/cpaa.2017015

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

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

Received  May 2016 Revised  July 2016 Published  November 2016

Fund Project: 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.

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 $\mathbb{R}^{n}$.

Citation: Saikat Mazumdar. Struwe's decomposition for a polyharmonic operator on a compact Riemannian manifold with or without boundary. Communications on Pure & Applied Analysis, 2017, 16 (1) : 311-330. doi: 10.3934/cpaa.2017015
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