完全非线性一致椭圆方程的边界爆破问题

Boundary blow-up problems for fully nonlinear uniformly elliptic equations

利用逼近的方法研究了完全非线性一致椭圆方程F(D2u)=g(x,u)在区域DRn内的爆破解,即当d(x,D)→0时,解u(x)→∞,得到了完全非线性一致椭圆方程爆破解的存在性、惟一性和不存在性。

The large solutions,i.e.solutions such that u（x）→∞ as d（x,D）→0,of fully nonlinear elliptic equations F（D2u）=g（x,u） in a domain DRn are investigated by the method of approximation.The existence,uniqueness and nonexistence of large solutions of fully nonlinear uniformly elliptic equations are obtained.