@article{Ghimenti2022, 
author = {Marco G. Ghimenti and Anna Maria Micheletti},
title = {Compactness and blow up results for doubly perturbed Yamabe problems on manifolds with non umbilic boundary},
year = {2022},
journal = {Electronic Research Archive},
volume = {30},
number = {4},
pages = {1209-1235},
keywords = {compactness, non umbilic boundary, Yamabe problem, blow up analysis},
url = {https://www.sciopen.com/article/10.3934/era.2022064},
doi = {10.3934/era.2022064},
abstract = {We study the stability of compactness of solutions for the Yamabe boundary problem on a compact Riemannian manifold with non umbilic boundary. We prove that the set of solutions of Yamabe boundary problem is a compact set when perturbing the mean curvature of the boundary from below and the scalar curvature with a function whose maximum is not too positive. In addition, we prove the counterpart of the stability result: there exists a blowing up sequence of solutions when we perturb the mean curvature from above or the mean curvature from below and the scalar curvature with a function with a large positive maximum.}
}