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Uniform Anti-maximum Principles

✍ Scribed by Ph Clément; G Sweers

Publisher
Elsevier Science
Year
2000
Tongue
English
Weight
266 KB
Volume
164
Category
Article
ISSN
0022-0396

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Cle ment and Peletier showed in [3] a result that reads for the Dirichlet Laplacian on bounded smooth domains 0/R n as follows. v For all f>0 with f # L p (0) and p>n, there is \* f >\* 1 , where \* 1 is the first eigenvalue, such that one finds for \* # (\* 1 , \* f ) that the solution of For \*<

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Strong maximum and anti-maximum principles are extended to weak L 2 (R 2 )solutions u of the Schro dinger equation &2u+q(x) u&\*u= f (x) in L 2 (R 2 ) in the following form: Let . 1 denote the positive eigenfunction associated with the principal eigenvalue \* 1 of the Schro dinger operator A=&2+q(x)