论文标题
关于Hessian类型的外部Dirichlet问题完全非线性椭圆方程
On the exterior Dirichlet problem for Hessian type fully nonlinear elliptic equations
论文作者
论文摘要
我们将表格$$ f（λ（d^2u））的一类完全非线性椭圆方程的外部差异问题处理，$ g（x），$$，在无穷大处有规定的渐近行为。 Caffarelli-nirenberg- Pruck \ cite {caffarelli1985}，Trudinger \ cite {Trudinger1995}以及许多其他方程进行了广泛研究，并且有许多其他关于Contical dirichletunity方法的讨论，并且在Continaluity Compution contunitun contunity方法上进行了$ cockaig f. In this paper, based on the Perron's method, we establish an exterior existence and uniqueness result for viscosity solutions of the equations by assuming $f$ to satisfy certain structure conditions as in \cite{Caffarelli1985,Trudinger1995}, which may embrace the well-known Monge--Ampère equations, Hessian equations and Hessian quotient equations as special cases but do not require the concavity.
We treat the exterior Dirichlet problem for a class of fully nonlinear elliptic equations of the form $$f(λ(D^2u))=g(x),$$ with prescribed asymptotic behavior at infinity. The equations of this type had been studied extensively by Caffarelli--Nirenberg--Spruck \cite{Caffarelli1985}, Trudinger \cite{Trudinger1995} and many others, and there had been significant discussions on the solvability of the classical Dirichlet problem via the continuity method, under the assumption that $f$ is a concave function. In this paper, based on the Perron's method, we establish an exterior existence and uniqueness result for viscosity solutions of the equations by assuming $f$ to satisfy certain structure conditions as in \cite{Caffarelli1985,Trudinger1995}, which may embrace the well-known Monge--Ampère equations, Hessian equations and Hessian quotient equations as special cases but do not require the concavity.
