Acta Mathematica Vietnamica
- Volume 49
- Volume 48
- Volume 47
- Volume 46
- Volume 45
- Volume 44
- Volume 43
- Volume 42
- Volume 41
- Volume 40
- Volume 39
- Volume 38
- Volume 37
- Volume 36
- Volume 35
- Volume 34
- Volume 33
- Volume 32
- Volume 31
- Volume 30
- Volume 29
- Volume 28
- Volume 27
- Volume 26
- Volume 25
- Volume 24
- Volume 23
- Volume 22
- Volume 21
- Volume 20
- Volume 19
- Volume 18
- Volume 17
- Volume 16
- Volume 15
- Volume 14
- Volume 13
- Volume 12
- Volume 11
- Volume 10
- Volume 9
- Volume 8
- Volume 7
- Volume 6
- Volume 5
- Volume 4
- Volume 3
- Volume 2
- Volume 1
Some Analytic Results for Kimura Diffusion Operators
Charles L. Epstein
,
Jon Wilkening
Abstract
In this note, we prove several analytical results about generalized Kimura diffusion operators, $L$, defined on compact manifolds with corners, $P$. It is shown that the $\mathcal C^{0}(P)$-graph closure of $L$ acting on $\mathcal C^{2}(P)$ always has a compact resolvent. In the $1 d$-case, where $P = [0,1]$, we also establish a gradient estimate $\|\partial _{x} f\|_{\mathcal C^{0}([0,1])}\leq C\| L f\|_{\mathcal C^{0}([0,1])}$, provided that $L$ has strictly positive weights at $\partial[0,1] = \{0,1\}$. This in turn leads to a precise characterization of the domain of the $\mathcal C^0$-graph closure in this case.