André Henrik Erhardt

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Visiting address Ullevål stadion Sognsveien 77 B 0855 OSLO
Postal address Postboks 1053 Blindern 0316 OSLO
Other affiliations Faculty of Mathematics and Natural Sciences (Student)

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:

Tags: Mathematics, Partial Differential Equations, Dynamical Systems, Mathematical Analysis, (Numerical) Bifurcation Analysis

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

Regularity 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

Published Oct. 30, 2017 10:52 AM - Last modified Feb. 14, 2018 1:16 PM