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

  • Edgard A. Pimentel
  • Makson S. Santos
Part of the Springer INdAM Series book series (SINDAMS, volume 28)


We survey recent asymptotic methods introduced in regularity theory for fully nonlinear elliptic equations. Our presentation focuses mainly on the recession function. We detail the role of this class of techniques through examples and results. Our applications include regularity in Sobolev and Hölder spaces. In addition, we produce a density result and examine ellipticity-invariant quantities, such as the Escauriaza’s exponent.


Fully nonlinear elliptic equations Regularity Theory Asymptotic Methods Recession Operator 

Mathematics Subject Classification (2010)

35J60 35B65 


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© Springer Nature Switzerland AG 2018

Authors and Affiliations

  1. 1.Department of MathematicsPontifical Catholic University of Rio de Janeiro – PUC-RioRio de JaneiroBrazil

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