# André Henrik Erhardt

My research focuses on **Partial Differential Equations**, **Calculus of Variations**, **Dynamical Systems** and Applications in the Life Sciences.

In the field of nonlinear PDEs I am working on existence and regularity theory for parabolic PDEs and obstacle problems. Here, I am interested amongst others in nonstandard growth problems motivated, e.g., by electro-rheological fluids.

Moreover, since 2014 I am extending my fields of interest to my second research area: dynamical systems, bifurcation theory, multiple time scale dynamics and geometric singular perturbation theory. One main application is the mathematical and numerical investigation of cardiac arrhythmia, e.g., the so-called early afterdepolarizations.

In general, I am interested in several applications and problems, e.g., from fluid mechanics or biology modelled by differential equations, i.e., ODEs as well as PDEs. My research is focused on Pure and Applied Mathematics.

**Research Interests:**

- Nonlinear PDEs and Dynamics
- Existence Theory
- Regularity Theory
- Stability Theory
- Bifurcation Theory
- (Geometric) Singular Perturbation Theory

**Further information about my research, mainly my publication list and citations, can be found here:**

**Full publication list is available on:**

## Publications

*The stability of parabolic problems with nonstandard p(x,t)-growth*. Mathematics, **5**(2017), no.4(50), p.1-14, DOI 10.3390/math5040050

*Compact embedding for p(x,t)-Sobolev spaces and existence theory to parabolic equations with p(x,t)-growth*. Rev Mat Complut, **30**(2017), no.1, p.35–61, DOI 10.1007/s13163-016-0211-4

R*egularity results for nonlinear parabolic obstacle problems with subquadratic growth. *J. Differential Equations, **261**(2016), no.12, p.6915–6949, DOI 10.1016/j.jde.2016.09.006

*Existence of solutions to parabolic problems with nonstandard growth and irregular obstacles*. Adv. Differential Equations, **21**(2016), no.5-6, p.463–504, link

*Higher integrability for solutions to parabolic problems with irregular obstacles and nonstandard growth*. J. Math. Anal. Appl., **435**(2016), no.2, p.1772–1803, DOI 10.1016/j.jmaa.2015.11.028

*Hölder estimates for parabolic obstacle problems*. Ann. Mat. Pura Appl. (4), **194**(2015), no.3, p.645–671, DOI 10.1007/s10231-013-0392-0

*Calderón-Zygmund theory for parabolic obstacle problems with nonstandard growth*. Adv. Nonlinear Anal., **3**(2014), no.1, p.15–44, DOI 10.1515/anona-2013-0024