Asymptotic Methods in Regularity Theory for Nonlinear Elliptic Equations: A Survey

Regularity estimates for nonlocal equations with an asymptotic property

“…The first feature we bring here is a lemma concerning homogeneity. The same ideas were presented in [8].…”

Improved regularity for the porous medium equation along zero level sets

“…Led by the works of E. Teixeira, J.-M. Urbano and their collaborators, the geometric tangential analysis has been proven instrumental in unveiling further layers of information on various classes of problems; see [5], [37], [29], [4], [3], [31], [32], [38], [34], just to mention a few references. We also allude to the survey papers [36], [30], [39] and the references therein. The present work is inspired by those methods and advances them further into the context of the porous medium equation.…”

Mostly Regularity Theory: Interfaces and Free Boundaries

“…We argue through geometric tangential methods; see, for instance, [59], [52], and [60]. See also [21].…”

“…See, for instance [3], [4], [61], [63], [62] just to cite a few. We also refer to the surveys [52], [64].…”

“…We emphasize that improved regularity under such small-jumps condition follows through a set of methods known as geometric tangential analysis. We refer the reader to the following survey papers on this class of techniques [59,52,60]. The problem examined in [1] profits from the existence of an associated functional and the properties derived for its minima.…”