Subscribe to the gold package and get unlimited access to Shamra Academy
Register a new userScale-invariant boundary Harnack principle on inner uniform domains in fractal-type spaces
129
0
0.0
(
0
)
Authors
Janna Lierl
Ask ChatGPT about the research
No Arabic abstract
We prove a scale-invariant boundary Harnack principle for inner uni- form domains in metric measure Dirichlet spaces. We assume that the Dirichlet form is symmetric, strongly local, regular, and that the volume doubling property and two-sided sub-Gaussian heat kernel bounds are satisfied. We make no assumptions on the pseudo-metric induced by the Dirichlet form, hence the underlying space can be a fractal space.
rate research
Read More
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 form operators that are not necessarily symmetric, and complement earlier results by H. Aikawa and A. Ancona.
This paper proves the strong parabolic Harnack inequality for local weak solutions to the heat equation associated with time-dependent (nonsymmetric) bilinear forms. The underlying metric measure Dirichlet space is assumed to satisfy the volume doubling condition, the strong Poincare inequality, and a cutoff Sobolev inequality. The metric is not required to be geodesic. Further results include a weighted Poincare inequality, as well as upper and lower bounds for non-symmetric heat kernels.
We investigate the Boundary Harnack Principle in Holder domains of exponent $alpha>0$ by the analytical method developed in our previous work A short proof of Boundary Harnack Principle.
We investigate the parabolic Boundary Harnack Principle for both divergence and non-divergence type operators by the analytical methods we developed in the elliptic context. Besides the classical case, we deal with less regular space-time domains, including slit domains.
Suppose that $E$ and $E$ denote real Banach spaces with dimension at least 2, that $Dsubset E$ and $Dsubset E$ are domains, and that $f: Dto D$ is a homeomorphism. In this paper, we prove the following subinvariance property for the class of uniform domains: Suppose that $f$ is a freely quasiconformal mapping and that $D$ is uniform. Then the image $f(D_1)$ of every uniform subdomain $D_1$ in $D$ under $f$ is still uniform. This result answers an open problem of Vaisala in the affirmative.
Log in to be able to interact and post comments
comments
Fetching comments
Sign in to be able to follow your search criteria
