Kernel estimates for elliptic operators with second-order discontinuous coefficients

We study parabolic problems associated to the second-order elliptic operator L = Δ + ( a - 1 ) ∑ i , j = 1 N x i x j | x | 2 D i j + c x | x | 2 · ∇ - b | x | - 2 with a > 0 and b , c real coefficients and prove kernel estimates for the transition kernel.

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Bibliographic Details
Published inJournal of evolution equations Vol. 17; no. 1; pp. 485 - 522
Main Authors Metafune, G., Sobajima, M., Spina, C.
Format Journal Article
LanguageEnglish
Published Cham Springer International Publishing 01.03.2017
Springer Nature B.V
Subjects
Analysis
Kernels
Mathematics
Mathematics and Statistics
Elliptic operators
35J70
Kernel estimates
Discontinuous coefficients
Analytic semigroups
35B50
35J25
47D07
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Summary:We study parabolic problems associated to the second-order elliptic operator L = Δ + ( a - 1 ) ∑ i , j = 1 N x i x j | x | 2 D i j + c x | x | 2 · ∇ - b | x | - 2 with a > 0 and b , c real coefficients and prove kernel estimates for the transition kernel.
ISSN:1424-3199
1424-3202
DOI:10.1007/s00028-016-0355-1