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

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PDE Models for Multi-Agent Phenomena

Part of the book series: Springer INdAM Series ((SINDAMS,volume 28))

Abstract

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.

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Authors and Affiliations

  1. Department of Mathematics, Pontifical Catholic University of Rio de Janeiro – PUC-Rio, Rio de Janeiro, Brazil

    Edgard A. Pimentel & Makson S. Santos

Authors
  1. Edgard A. Pimentel
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  2. Makson S. Santos
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Corresponding author

Correspondence to Edgard A. Pimentel .

Editor information

Editors and Affiliations

  1. Ceremade, Université Paris-Dauphine, Paris, France

    Pierre Cardaliaguet

  2. Dept. of Mathematics, Universitá di Roma “Tor Vergata”, Roma, Italy

    Alessio Porretta

  3. Dept. of Mathematics “F. Casorati”, University of Pavia, Pavia, Italy

    Francesco Salvarani

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Pimentel, E.A., Santos, M.S. (2018). Asymptotic Methods in Regularity Theory for Nonlinear Elliptic Equations: A Survey. In: Cardaliaguet, P., Porretta, A., Salvarani, F. (eds) PDE Models for Multi-Agent Phenomena. Springer INdAM Series, vol 28. Springer, Cham. https://doi.org/10.1007/978-3-030-01947-1_8

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