Uniqueness of Solutions to -Delta - qu = 0.
Abstract
Conditions are given for the function q(x) which guarantee uniqueness of solutions to -Delta u(x) + lambda sub 0 u(x) - q(x)u(x) = f, where lambda sub 0 > or = 0 is a constant. The cases for solutions in H(1) and L(2) are considered separately. In fact, existence of H(1) solutions under the additional assumptions q(x) > or = 0 and f is an element of L(2) are proven. These results are applied to the problem of essential selfadjointness for a class of Schrodinger operators and an interesting generalization of a result due to Kato is proven. Gaveau proved a result similar to this on L(2) uniqueness. His proof, however, depended on a probabalistic argument, while in contrast there is no probability theory used in these proofs.
Document Details
- Document Type
- Technical Report
- Publication Date
- Feb 01, 1978
- Accession Number
- ADA054546
Entities
People
- Robert E. Jensen
Organizations
- University of Wisconsin–Madison