Heat kernel for non-local operators with variable order
نویسندگان
چکیده
منابع مشابه
Harnack Inequalities for Non-local Operators of Variable Order
We consider harmonic functions with respect to the operator Lu(x) = ∫ [u(x+ h)− u(x)− 1(|h|≤1)h · ∇u(x)]n(x, h) dh. Under suitable conditions on n(x, h) we establish a Harnack inequality for functions that are nonnegative and harmonic in a domain. The operator L is allowed to be anisotropic and of variable order.
متن کاملStability of Dirichlet Heat Kernel Estimates for Non-local Operators under Feynman-kac Perturbation
Abstract. In this paper we show that Dirichlet heat kernel estimates for a class of (not necessarily symmetric) Markov processes are stable under nonlocal Feynman-Kac perturbations. This class of processes includes, among others, (reflected) symmetric stable-like processes in closed d-sets in Rd, killed symmetric stable processes, censored stable processes in C1,1 open sets, as well as stable p...
متن کاملHeat trace of non-local operators
This paper extends results of M. van den Berg on two-term asymptotics for the trace of Schödinger operators when the Laplacian is replaced by non-local (integral) operators corresponding to rotationally symmetric stable processes and other closely related Lévy processes. CONTENTS
متن کاملA Note on Heat Kernel Estimates for Second-order Elliptic Operators
We study fundamental solutions to second order parabolic systems of divergence type with time independent coefficients, and give another proof of a result by Auscher, McIntosh and Tchamitchian on the Gaussian bounds for the heat kernels of second order elliptic operators in divergence form with complex bounded measurable coefficients.
متن کاملKernel Asymptotics of Exotic Second-Order Operators
The Navier–Lamé operator of classical elasticity, μ∆v+(λ+μ)∇(∇·v), is the simplest example of a linear differential operator whose second-order terms involve a coupling among the components of a vector-valued function. Similar operators on Riemannian manifolds arise in conformal geometry and in quantum gravity. (In the latter context they have come to be called “nonminimal”, but “exotic” is pro...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Stochastic Processes and their Applications
سال: 2020
ISSN: 0304-4149
DOI: 10.1016/j.spa.2019.10.004