Janna Lierl

I am an Assistant Professor of Mathematics at the University of Connecticut at Storrs. My research interests are in Probability, Analysis, PDE's.

I received my PhD from Cornell in 2012. I was a Hausdorff postdoc at HCM in Bonn 2012-2014, and a J. J. Uhl Research Assistant Professor at the University of Illinois at Urbana-Champaign 2014-2016. I am supported by a Collaboration Grant from the Simons Foundation 2018-2023.

I am on the job market.

## Contact

janna.lierl 'at' uconn.edu

Department of Mathematics

341 Mansfield Road

Storrs, CT, 06269

Office hours: See HuskyCT.

## Preprints

- A. Biswas, J. Lierl,
Faber-Krahn type inequalities and uniqueness of positive solutions on metric measure spaces,submitted 2018, arXiv:1810.11577

- J. Lierl,
Local behavior of solutions of quasilinear parabolic equations on metric space, submitted 2017, arxiv:1708.06329- J. Lierl,
Parabolic Harnack inequality for time-dependent non-symmetric Dirichlet forms, submitted 2017, preprint available upon request.- J. Lierl,
The Dirichlet heat kernel in inner uniform domains in fractal-type spaces, submitted 2016, preprint available upon request.

## Publications

- J. Lierl, S. Steinerberger,
A Local Faber-Krahn inequality and Applications to Schrödinger's Equation,Comm. Partial Differential Equations43 (2018), no.1, 66-81.- J. Lierl, K.-T. Sturm,
Neumann heat flow and gradient flow for the entropy on non-convex domains,Calc. Var. Partial Differential Equations57 (2018), no.1, Art. 25, 22pp.- J. Lierl,
Parabolic Harnack inequality on fractal-type metric measure Dirichlet spaces,Rev. Mat. Iberoam.34 (2018), no.2, 687–738.- J. Lierl,
Scale-invariant boundary Harnack principle on inner uniform domains in fractal-type spaces,Potential Analysis43 (2015), no. 4, 717–747. Original version of this paper as submitted to Potential Analysis in June 2015.- J. Lierl, L. Saloff-Coste,
The Dirichlet heat kernel in inner uniform domains: local results, compact domains and non-symmetric forms,J. Funct. Anal.266 (2014), no. 7, 4189–4235.- J. Lierl, L. Saloff-Coste,
Scale-invariant boundary Harnack principle in inner uniform domains,Osaka J. Math.51 (2014), no. 3, 619–656.- F. Conrad, M. Grothaus, J. Lierl, O. Wittich,
Convergence of Brownian motion with a scaled Dirac delta potential,Proc. Edinb. Math. Soc.(2) 55 (2012), no. 2, 403–427.