Kernel and eigenfunction estimates for some second order elliptic operators
Language
en
Article de revue
This item was published in
Australian Journal of Mathematical Analysis and Applications. 2012, vol. 387, p. 799-806
Austral Internet Publishing
English Abstract
For a potential V such that V (x) |x|α with α > 2 we prove that the heat kernel kt (x, y) associated to the uniformly elliptic operator A =− nj ,k=1 ∂k(a jk∂ j ) + V satisfies the estimate kt (x, y) Ce−μ0tect−b e− 2 √ θ ...Read more >
For a potential V such that V (x) |x|α with α > 2 we prove that the heat kernel kt (x, y) associated to the uniformly elliptic operator A =− nj ,k=1 ∂k(a jk∂ j ) + V satisfies the estimate kt (x, y) Ce−μ0tect−b e− 2 √ θ α+2 |x|1+α2 |x|α4 +n−1 2 e− 2 √ θ α+2 |y|1+α2 |y|α4 +n−1 2 for large x, y ∈ Rn and all t > 0. Here 0 < θ 1 is an appropriate constant, b > α+2 α−2 and μ0 is the first eigenvalue of A. We also obtain an estimate for large |x| of the eigenfunctions of A.Read less <
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