Alt, H.W., Caffarelli, L.A. and Friedman, A. (1984) Variational Problems with Two Phases and Their Free Boundaries. Transactions of the AMS, 282, 431-461.
https://doi.org/10.1090/S0002-9947-1984-0732100-6

has been cited by the following article:

• TITLE: Uniform Hölder Bounds for Competition Systems with Strong Interaction on a Subdomain

  AUTHORS: Jiahao Ni, Shan Zhang

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

  JOURNAL NAME: Journal of Applied Mathematics and Physics, Vol.11 No.6, June 7, 2023

  ABSTRACT: 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.