Polynomial decay in $W^{2,\varepsilon}$ estimates for viscosity supersolutions of fully nonlinear elliptic equations

Nam Q. Le

Polynomial decay in $W^{2,\varepsilon}$ estimates for viscosity supersolutions of fully nonlinear elliptic equations

Analysis of PDEs 2018-09-11 v3

Authors: Nam Q. Le

Abstract

We prove $W^{2,\varepsilon}$ estimates for viscosity supersolutions of fully nonlinear, uniformly elliptic equations where $\varepsilon$ decays polynomially with respect to the ellipticity ratio of the equations. Our result is related to a conjecture of Armstrong-Silvestre-Smart [Comm. Pure Appl. Math. 65 (2012), no. 8, 1169--1184] which predicts a linear decay for $\varepsilon$ with respect to the ellipticity ratio of the equations.

Keywords

W^{2,epsilon} estimates viscosity supersolutions fully nonlinear elliptic equations uniform ellipticity polynomial decay

Cite

@article{arxiv.1805.08135,
  title  = {Polynomial decay in $W^{2,\varepsilon}$ estimates for viscosity supersolutions of fully nonlinear elliptic equations},
  author = {Nam Q. Le},
  journal= {arXiv preprint arXiv:1805.08135},
  year   = {2018}
}

Comments

v3: final version incorporating comments/suggestions from referee reports; to be published in Math. Res. Lett

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