26 citations · 77 across the 23 of their papers we have counts for
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Boundary Lipschitz Regularity and the Hopf Lemma on Reifenberg Domains for Fully Nonlinear Elliptic Equations
Yuanyuan Lian, Wenxiu Xu, Kai Zhang
In this paper, we prove the boundary Lipschitz regularity and the Hopf Lemma by a unified method on Reifenberg domains for fully nonlinear elliptic equations. Precisely, if the dom…
A simple proof of the transcendence of the trigonometric functions
Yuanyuan Lian, Kai Zhang
In this note, we give a simple proof that the values of the trigonometric functions at any nonzero rational number are transcendental numbers.
Regularity for fully nonlinear elliptic equations with oblique boundary conditions
Dongsheng Li, Kai Zhang
In this paper, we obtain a series of regularity results for viscosity solutions of fully nonlinear elliptic equations with oblique derivative boundary conditions. In particular, we…
On the boundary Hölder regularity for the infinity Laplace equation
Leyun Wu, Yuanyuan Lian, Kai Zhang
In this note, we prove the boundary Hölder regularity for the infinity Laplace equation under a proper geometric condition. This geometric condition is quite general, and the exter…
A note on the Harnack inequality for elliptic equations in divergence form
Dongsheng Li, Kai Zhang
In 1957, De Giorgi [3] proved the Hölder continuity for elliptic equations in divergence form and Moser [7] gave a new proof in 1960. Next year, Moser [8] obtained the Harnack ineq…
Pointwise Boundary Differentiability of Solutions of Elliptic Equations
Yongpan Huang, Dongsheng Li, Kai Zhang
In this paper, we give pointwise geometric conditions on the boundary which guarantee the differentiability of the solution at the boundary. Precisely, the geometric conditions are…
interior estimates of fully nonlinear elliptic equations
Dongsheng Li, Kai Zhang
In this paper, we generalize the interior estimates of fully nonlinear elliptic equations that were obtained by Caffarelli in [1]. The generalizations are carried out in…
An Optimal Geometric Condition on Domains for Boundary Differentiability of Solutions of Elliptic Equations
Dongsheng Li, Kai Zhang
In this paper, a geometric condition on domains will be given which guarantees the boundary differentiability of solutions of elliptic equations, that is, the solutions are differe…
Boundary Pointwise and Regularity for Fully Nonlinear Elliptic Equations
Yuanyuan Lian, Kai Zhang
In this paper, we obtain the boundary pointwise and regularity for viscosity solutions of fully nonlinear elliptic equations. I.e., If is …