A note on a class of higher order conformally covariant equations
Sun-Yung Alice Chang Wenxiong Chen
In this paper, we study the higher order conformally covariant equation

$(- \Delta )^{\frac{n}{2}} w = (n -1)! e^{n w} x \in R^n$

for all even dimensions n.

$\alpha = \frac{1}{|S^n|} \int_{R^n} e^{n w} dx .$

We prove, for every $0 < \alpha < 1$, the existence of at least one solution. In particular, for $ n = 4$, we obtain the existence of radial solutions.

keywords: non-uniqueness variational method. Higher order semilinear elliptic equations conformally covariant equations
A Liouville problem for the Sigma-2 equation
Sun-Yung Alice Chang Yu Yuan
We show that any global convex solution to the Sigma-2 equation must be quadratic.
keywords: Sigma-2 equation Legendre-Lewy transformation Evans-Krylov-Safonov theory.
Principal curvature estimates for the convex level sets of semilinear elliptic equations
Sun-Yung Alice Chang Xi-Nan Ma Paul Yang
We give a positive lower bound for the principal curvature of the strict convex level sets of harmonic functions in terms of the principal curvature of the domain boundary and the norm of the boundary gradient. We also extend this result to a class of semi-linear elliptic partial differential equations under certain structure condition.
keywords: semilinear elliptic equation. Curvature estimate level sets

Year of publication

Related Authors

Related Keywords

[Back to Top]