A Sobolev inequality with remainder term and critical equations on domains with topology for the polyharmonic operator

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Existence and nonexistence results for critical growth biharmonic elliptic equations (2003, background): “Recently, corresponding results have been found also in the higher order case: see [9] for problem (5) and [ 3 ] for the polyharmonic analogue of (6) under Dirichlet boundary conditions.”
Higher-order Sobolev embeddings and isoperimetric inequalities (2013, background): “The contributions to this field now constitute the corpus of a vast literature, which includes the papers [1, 4, 6, 10, 11, 15, 16, 20, 22, 24, 27, 31, 33, 39, 40, 45, 47, 49, 50, 52, 53, 54, 59, 60, 68, 89] and the monographs [17, 19, 21, 48, 67, 78].”
Remainder terms in the fractional Sobolev inequality (2012, methodology): “The general idea described here had already been used in [3, 5, 22], but the proofs of the normal non-degeneracy property in these papers strongly rely on the assumption that s is an even positve integer and therefore the eigenvalue problem for Φ′′(U) can be written as a differential equation.”
Sharp gradient stability for the Sobolev inequality (2020, background): “Introduction Motivated by important applications to problems in the calculus of variations and evolution PDEs, in recent years there has been a growing interest around the understanding of quantitative stability for functional/geometric inequalities, see for instance [3, 2, 8, 27, 28, 21, 9, 22, 29,”