# Spectral gap estimates for Brownian motion on domains with sticky-reflecting boundary diffusion

@inproceedings{Konarovskyi2021SpectralGE, title={Spectral gap estimates for Brownian motion on domains with sticky-reflecting boundary diffusion}, author={Vitalii Konarovskyi and Victor Marx and M. Renesse}, year={2021} }

Introducing an interpolation method we estimate the spectral gap for Brownian motion on general domains with sticky-reflecting boundary diffusion associated to the first nontrivial eigenvalue for the Laplace operator with corresponding Wentzell-type boundary condition. In the manifold case our proofs involve novel applications of the celebrated Reilly formula.

#### References

SHOWING 1-10 OF 40 REFERENCES

Stochastic differential equations with sticky reflection and boundary diffusion

- Mathematics
- 2017

We construct diffusion processes in bounded domains Ω with sticky reflection at the boundary Γ in use of Dirichlet forms. In particular, the occupation time on the boundary is positive. The… Expand

Maximal regularity, analytic semigroups, and dynamic and general Wentzell boundary conditions with a diffusion term on the boundary

- Mathematics
- Annali di Matematica Pura ed Applicata (1923 -)
- 2019

We show maximal regularity results concerning parabolic systems with dynamic boundary conditions and a diffusion theorem on the boundary in the framework of $$L^p$$ L p spaces, $$1<p<\infty $$ 1 < p… Expand

Reversible Coalescing-Fragmentating Wasserstein Dynamics on the Real Line

- Mathematics
- 2017

We introduce a family of reversible fragmentating-coagulating processes of particles of varying size-scaled diffusivity with strictly local interaction on the real line. The construction is based on… Expand

Construction and analysis of a sticky reflected distorted Brownian motion

- Mathematics
- 2014

We give a Dirichlet form approach for the construction of a distorted Brownian motion in $E:=[0,\infty)^n$, $n\in\mathbb{N}$, where the behavior on the boundary is determined by the competing effects… Expand

The Laplacian on C( ) with generalized Wentzell boundary conditions

- Mathematics
- 2003

In this note we prove that the Laplacian with generalized Wentzell boundary condi- tions on an open bounded regular domainin Rm defined by

An isoperimetric inequality for the second eigenvalue of the Laplacian with Robin boundary conditions

- Mathematics
- 2008

We prove that the second eigenvalue of the Laplacian with Robin boundary conditions is minimized among all bounded Lipschitz domains of fixed volume by the domain consisting of the disjoint union of… Expand

Overdamped limit of generalized stochastic Hamiltonian systems for singular interaction potentials

- Mathematics
- Journal of Evolution Equations
- 2019

First, weak solutions of generalized stochastic Hamiltonian systems (gsHs) are constructed via essential m -dissipativity of their generators on a suitable core. For a scaled gsHs we prove… Expand

Exact constants in Poincaré type inequalities for functions with zero mean boundary traces

- Mathematics
- 2012

In this paper, we investigate Poincare type inequalities for the functions having zero mean value on the whole boundary of a Lipschitz domain or on a measurable part of the boundary. We find exact… Expand

DIRICHLET FORMS FOR GENERAL WENTZELL BOUNDARY CONDITIONS, ANALYTIC SEMIGROUPS, AND COSINE OPERATOR FUNCTIONS

- Mathematics
- 2006

The aim of this paper is to study uniformly elliptic operators with general Wentzell boundary conditions in suitable L p -spaces by using the ap- proach of sesquilinear forms. We use dierent tools to… Expand

Composite media and asymptotic dirichlet forms

- Mathematics
- 1994

We introduce a metric topology on the space of Dirichlet forms and study compactness and closure properties of families of local and non-local forms.