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Kernel and eigenfunction estimates for some second order elliptic operators
RHANDI, Abdelaziz
Department of Information Engineering, Electrical Engineering and Applied Mathematics [DIEM]
Department of Information Engineering, Electrical Engineering and Applied Mathematics [DIEM]
RHANDI, Abdelaziz
Department of Information Engineering, Electrical Engineering and Applied Mathematics [DIEM]
< Reduce
Department of Information Engineering, Electrical Engineering and Applied Mathematics [DIEM]
Language
en
Article de revue
This item was published in
Journal of Mathematical Analysis and Applications. 2012, vol. 387, n° 2, p. 799-806
Elsevier
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 <
English Keywords
Heat kernels Schrödinger operators Eigenfunctions Log-Sobolev inequality
Origin
Hal imported