$C^{1,\alpha}$ regularity of solutions of degenerate fully non-linear elliptic equations

Cyril Imbert; L. Silvestre

doi:10.1016/j.aim.2012.07.033

$C^{1,\alpha}$ regularity of solutions of degenerate fully non-linear elliptic equations

Analysis of PDEs 2012-11-27 v1

Authors: Cyril Imbert , L. Silvestre

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Abstract

In the present paper, a class of fully non-linear elliptic equations are considered, which are degenerate as the gradient becomes small. H\"older estimates obtained by the first author (2011) are combined with new Lipschitz estimates obtained through the Ishii-Lions method in order to get $C^{1,\alpha}$ estimates for solutions of these equations.

Keywords

degenerate fully non-linear elliptic equations regularity Hölder estimates Lipschitz estimates Ishii-Lions method

Cite

@article{arxiv.1201.3739,
  title  = {$C^{1,\alpha}$ regularity of solutions of degenerate fully non-linear elliptic equations},
  author = {Cyril Imbert and L. Silvestre},
  journal= {arXiv preprint arXiv:1201.3739},
  year   = {2012}
}

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