Blow-up Theory for Elliptic PDEs in Riemannian Geometry

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On the global well-posedness of energy-critical Schr\"odinger equations in curved spaces (2010, background): “This approach was already used in the study of elliptic equations, first in the subcritical case (where the scaling limits are easier) by Gidas-Spruck [26] and also in the H1 critical setting, see for example DruetHebey-Robert [24], Hebey-Vaugon [30], Schoen [47] and (many) references therein for ex”
Mathematical Analysis of Partial Differential Equations Modeling Electrostatic MEMS (2010, background): “An important and comprehensive contribution in this direction can be found in the monograph [57] by O.”
Concentration estimates for Emden-Fowler equations with boundary singularities and critical growth (2005, methodology): “We only sketch the proof. Details are available in [ 15 ].”
Existence and orbital stability of the ground states with prescribed mass for the $L^2$-critical and supercritical NLS on bounded domains (2013, methodology): “MR 84i:81015 Zbl 0513.35007 [Druet et al. 2004] O. Druet, E. Hebey, and F. Robert, Blow-up theory for elliptic PDEs in Riemannian geometry, Mathematical Notes 45, Princeton University Press, 2004.”
A priori estimates and application to the symmetry of solutions for critical $p$-Laplace equations (2014, background): “Possible references in book form on this subject and its applications in case p = 2 are Druet–Hebey–Robert [8], Ghoussoub [10], and Struwe [27].”