Author(s)

Jiahao Ni, Shan Zhang^*

School of Applied Mathematics, Nanjing University of Finance & Economics, Nanjing, China.

We prove the uniform Hölder bounds of solutions to a singularly perturbed elliptic system arising in competing models in population dynamics. In this system, two species compete to some extent throughout the whole domain but compete strongly on a subdomain. The proof relies upon the blow up technique and the monotonicity formula by Alt, Caffarelli and Friedman.

Singularly Perturbation, Subdomain, Free Boundary Problem, Liouville Type Theorem

Ni, J. and Zhang, S. (2023) Uniform Hölder Bounds for Competition Systems with Strong Interaction on a Subdomain. Journal of Applied Mathematics and Physics, 11, 1525-1540. doi: 10.4236/jamp.2023.116100.