A Riemannian Off-diagonal Heat Kernel Bound for Uniformly Elliptic Operators
نویسنده
چکیده
We find a Gaussian off-diagonal heat kernel estimate for uniformly elliptic operators with measurable coefficients acting on regions Ω ⊆ R , where the order 2m of the operator satisfies N < 2m. The estimate is expressed using certain Riemannian-type metrics, and a geometrical result is established allowing conversion of the estimate into terms of the usual Riemannian metric on Ω. Work of Barbatis [1] is applied to find the best constant in this expression.
منابع مشابه
A Riemannian O - Diagonal Heat Kernel Bound forUniformly Elliptic OperatorsM
We nd a Gaussian oo-diagonal heat kernel estimate for uniformly elliptic operators with measurable coeecients acting on regions R N , where the order 2m of the operator satisses N < 2m. The estimate is expressed using certain Riemannian-type metrics, and a geometrical result is established allowing conversion of the estimate into terms of the usual Riemannian metric on. Work of Barbatis 1] is a...
متن کاملProof of the symmetry of the off-diagonal heat-kernel and Hadamard’s expansion coefficients in general C∞ Riemannian manifolds
Abstract: We consider the problem of the symmetry of the off-diagonal heat-kernel coefficients as well as the coefficients corresponding to the short-distance-divergent part of the Hadamard expansion in general smooth (analytic or not) manifolds. The requirement of such a symmetry played a central rôle in the theory of the point-splitting one-loop renormalization of the stress tensor in either ...
متن کاملUniformly Elliptic Operators on Riemannian Manifolds
Given a Riemannian manifold (M, g), we study the solutions of heat equations associated with second order differential operators in divergence form that are uniformly elliptic with respect to g . Typical examples of such operators are the Laplace operators of Riemannian structures which are quasi-isometric to g . We first prove some Poincare and Sobolev inequalities on geodesic balls. Then we u...
متن کاملAlgebra properties for Sobolev spaces- Applications to semilinear PDE's on manifolds
In this work, we aim to prove algebra properties for generalized Sobolev spaces W ∩L on a Riemannian manifold, whereW s,p is of Bessel-typeW s,p := (1+L)(L) with an operator L generating a heat semigroup satisfying off-diagonal decays. We don’t require any assumption on the gradient of the semigroup. To do that, we propose two different approaches (one by a new kind of paraproducts and another ...
متن کاملThe Solution of the Kato Problem for Divergence Form Elliptic Operators with Gaussian Heat Kernel Bounds
We solve the Kato problem for divergence form elliptic operators whose heat kernels satisfy a pointwise Gaussian upper bound. More precisely, given the Gaussian hypothesis, we establish that the domain of the square root of a complex uniformly elliptic operator L = −div(A∇) with bounded measurable coefficients in Rn is the Sobolev space H1(Rn) in any dimension with the estimate ‖ √ Lf‖2 ∼ ‖∇f‖2...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 1998