Uniform bounds for higher-order semilinear problems in conformal dimension

A-priori bounds for quasilinear problems in critical dimension

“…We note that a similar approach has been also applied by Mancini and the author in [24] to study higher-order problems. Throughout all the paper, Ω is a bounded and strictly convex domain in R N with C 1,α boundary and the nonlinearity f satisfies the following conditions:…”

“…The argument is based on a blow-up method inspired by [23] and developed in [24]: supposing the existence of an unbounded sequence of solutions, we define a rescaled sequence which locally converges to a solution of a Liouville's equation on R N . Then, we have to distinguish two cases according to the growth of f .…”