A Faber-Krahn inequality for solutions of Schrodinger%26apos;s equation

作者：De Carli L; Hudson S M^*

来源：Advances in Mathematics, 2012, 230(4-6): 2416-2427.

DOI：10.1016/j.aim.2012.04.014

• Faber-Krahn
• Schrodinger
• Bounded potential
• Unique continuation
• First eigenvalue

We consider nontrivial solutions of -Delta u(x) = V(x)u(x), where u equivalent to 0 on the boundary of a bounded open region D subset of R-n, and V(x) is an element of L-infinity(D). We prove a sharp relationship between parallel to V parallel to(infinity) and the measure of D, which generalizes the well-known Faber-Krahn theorem. We also prove some geometric properties of the zero sets of the solution of the Schrodinger equation -Delta u(x) = V(x)u(x).

• 出版日期2012-8