4 citations · 7 across the 5 of their papers we have counts for
9 papers
Faber-Krahn type inequalities and uniqueness of positive solutions on metric measure spaces
Anup Biswas, Janna Lierl
We consider a general class of metric measure spaces equipped with a regular Dirichlet form and then provide a lower bound on the hitting time probabilities of the associated Hunt…
A Local Faber-Krahn inequality and Applications to Schrödinger's Equation
Janna Lierl, Stefan Steinerberger
We prove a local Faber-Krahn inequality for solutions to the Dirichlet problem for on an arbitrary domain in . Suppose a solution assumes a global…
Local behavior of solutions of quasilinear parabolic equations on metric spaces
Janna Lierl
We introduce a notion of quasilinear parabolic equations over metric measure spaces. Under sharp structural conditions, we prove that local weak solutions are locally bounded and s…
Neumann heat flow and gradient flow for the entropy on non-convex domains
Janna Lierl, Karl-Theodor Sturm
For large classes of non-convex subsets in or in Riemannian manifolds or in RCD-spaces we prove that the gradient flow for the Boltzmann entro…
Parabolic Harnack inequality on fractal-type metric measure Dirichlet spaces
Janna Lierl
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…
The Dirichlet heat kernel in inner uniform domains: local results, compact domains and non-symmetric forms
Janna Lierl, Laurent Saloff-Coste
This paper provides sharp Dirichlet heat kernel estimates in inner uniform domains, including bounded inner uniform domains, in the context of certain (possibly non-symmetric) bili…
Parabolic Harnack inequality for time-dependent non-symmetric Dirichlet forms
Janna Lierl, Laurent Saloff-Coste
In the context of a metric measure Dirichlet space satisfying volume doubling and Poincaré inequality, we prove the parabolic Harnack inequality for weak solutions of the heat equa…
Scale-invariant boundary Harnack principle on inner uniform domains in fractal-type spaces
Janna Lierl
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…
Scale-invariant Boundary Harnack Principle in Inner Uniform Domains
Janna Lierl, Laurent Saloff-Coste
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 ap…