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

Abstract : In the present paper, a class of fully non-linear elliptic equations are considered, which are degenerate as the gradient becomes small. Hölder 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.
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Cyril Imbert, L. Silvestre. $C^{1,\alpha}$ regularity of solutions of degenerate fully non-linear elliptic equations. Advances in Mathematics, Elsevier, 2012, 233, pp.196-206. ⟨10.1016/j.aim.2012.07.033⟩. ⟨hal-00660912⟩

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