# Heat kernel estimates on manifolds with ends with mixed boundary condition

@inproceedings{Dautenhahn2021HeatKE, title={Heat kernel estimates on manifolds with ends with mixed boundary condition}, author={Emily S. Dautenhahn and Laurent Saloff-Coste}, year={2021} }

We obtain two-sided heat kernel estimates for Riemannian manifolds with ends with mixed boundary condition, provided that the heat kernels for the ends are well understood. These results extend previous results of Grigor’yan and Saloff-Coste by allowing for Dirichlet boundary condition. The proof requires the construction of a global harmonic function which is then used in the h-transform technique.

## References

SHOWING 1-10 OF 25 REFERENCES

### THE HEAT EQUATION ON NONCOMPACT RIEMANNIAN MANIFOLDS

- Mathematics
- 1992

The behavior of the Green function G(x, y, t) of the Cauchy problem for the heat equation on a connected, noncompact, complete Riemannian manifold is investigated. For manifolds with boundary it is…

### Widder’s Representation Theorem for Symmetric Local Dirichlet Spaces

- Mathematics
- 2014

In classical PDE theory, Widder’s theorem gives a representation for non-negative solutions of the heat equation on $$\mathbb{R }^n$$. We show that an analogous theorem holds for local weak solutions…

### Neumann and Dirichlet Heat Kernels in Inner Uniform Domains

- Mathematics
- 2011

— This monograph focuses on the heat equation with either the Neumann or the Dirichlet boundary condition in unbounded domains in Euclidean space, Rie-mannian manifolds, and in the more general…

### Scale-invariant Boundary Harnack Principle in Inner Uniform Domains

- Mathematics
- 2011

We prove a scale-invariant boundary Harnack principle in inner uniform domains in the context of local regular Dirichlet spaces. For inner uniform Euclidean domains, our results apply to divergence…

### Boundary Harnack principle and elliptic Harnack inequality

- MathematicsJournal of the Mathematical Society of Japan
- 2019

We prove a scale-invariant boundary Harnack principle for inner uniform domains over a large family of Dirichlet spaces. A novel feature of our work is that our assumptions are robust to time changes…

### Heat kernel on connected sums of Riemannian manifolds

- Mathematics
- 1999

This note is about the heat kernel on a connected sum M of non-compact manifolds M1, M2, . . . ,Mk assuming that one knows enough about the heat kernels for each Mi individually (which is the case…

### HEAT KERNEL ON MANIFOLDS WITH ENDS

- Mathematics
- 2009

Nous obtenons des bornes inferieures et superieures du noyau de la chaleur sur des varietes riemanniennes non-paraboliques a bouts, sous l'hypothese que sur chaque bout, separement, une estimation de…

### Aspects of Sobolev-type inequalities

- Mathematics
- 2001

Preface Introduction 1. Sobolev inequalities in Rn 2. Moser's elliptic Harnack Inequality 3. Sobolev inequalities on manifolds 4. Two applications 5. Parabolic Harnack inequalities.

### Analysis on local Dirichlet spaces. I. Recurrence, conservativeness and Lp-Liouville properties.

- Mathematics
- 1994

The basic object for the sequel is a fixed regul r Dirichlet form S with domain Q) ( } on a real Hubert space H = L(X, m). The underlying topological space X is a locally compact separable Hausdorff…