Expand all
Collapse all
|
Results 1 - 2 of 2 |
1. CJM 2004 (vol 56 pp. 655)
|
On the Neumann Problem for the Schrödinger Equations with Singular Potentials in Lipschitz Domains We consider the Neumann problem for the Schr\"odinger equations $-\Delta u+Vu=0$,
with singular nonnegative potentials $V$ belonging to the reverse H\"older class
$\B_n$, in a connected Lipschitz domain $\Omega\subset\mathbf{R}^n$. Given
boundary data $g$ in $H^p$ or $L^p$ for $1-\epsilon Keywords:Neumann problem, Schrödinger equation, Lipschitz, domain, reverse Hölder class, $H^p$ space Categories:42B20, 35J10 |
2. CJM 1998 (vol 50 pp. 487)
|
On the Liouville property for divergence form operators In this paper we construct a bounded strictly positive
function $\sigma$ such that the Liouville property fails for the
divergence form operator $L=\nabla (\sigma^2 \nabla)$. Since in
addition $\Delta \sigma/\sigma$ is bounded, this example also gives a
negative answer to a problem of Berestycki, Caffarelli and Nirenberg
concerning linear Schr\"odinger operators.
Categories:31C05, 60H10, 35J10 |