论文标题
非均匀椭圆方程的强大最大原理和边界估计值
Strong maximum principle and boundary estimates for nonhomogeneous elliptic equations
论文作者
论文摘要
我们简单地证明了在$$ f（x，u，u，du，d^2u）表格上完全非线性椭圆pdes的粘度亚物物的强大最大原理证明，在方程式上适当的结构条件下，允许在梯度项上实现非lipschitz增长的结构条件。在光滑边界的情况下，我们还证明了Hopf引理，边界竖琴不等式和边界一部分上消失的正粘度解决方案与边界附近的距离函数相当。我们的结果适用于可变指数$ p $ -laplacian的特征值问题的弱解决方案。
We give a simple proof of the strong maximum principle for viscosity subsolutions of fully nonlinear elliptic PDEs on the form $$ F(x,u,Du,D^2u) = 0 $$ under suitable structure conditions on the equation allowing for non-Lipschitz growth in the gradient terms. In case of smooth boundaries, we also prove the Hopf lemma, the boundary Harnack inequality and that positive viscosity solutions vanishing on a portion of the boundary are comparable with the distance function near the boundary. Our results apply to weak solutions of an eigenvalue problem for the variable exponent $p$-Laplacian.
