论文标题
Vázquez的最大原理和椭圆形PDE的Landis猜想具有无限系数
The Vázquez maximum principle and the Landis conjecture for elliptic PDE with unbounded coefficients
论文作者
论文摘要
我们开发了一种新的，统一的方法来解决有关椭圆PDE的以下两个经典问题：具有非lipschitz非线性方程的强大最大原理，以及在整个空间或外部域中最多最大的溶液衰减。我们的结果适用于在许多以前的结果都需要有限成分的情况下，在许多情况下，具有局部无界低阶系数的差异和非散发器操作员。我们的方法允许相对简单且简短的证明，基于（弱）harnack不平等，在我们确定的方程式和域的大小的较低阶段，常数的最佳依赖性。
We develop a new, unified approach to the following two classical questions on elliptic PDE: the strong maximum principle for equations with non-Lipschitz nonlinearities, and the at most exponential decay of solutions in the whole space or exterior domains. Our results apply to divergence and nondivergence operators with locally unbounded lower-order coefficients, in a number of situations where all previous results required bounded ingredients. Our approach, which allows for relatively simple and short proofs, is based on a (weak) Harnack inequality with optimal dependence of the constants in the lower-order terms of the equation and the size of the domain, which we establish.
