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Caffarelli, L.A. and Lin, F. (2008) Singularly Perturbed Elliptic Systems and Multi-Valued Harmonic Functions with Free Boundaries. Journal of the American Mathematical Society, 21, 847-862.
https://doi.org/10.1090/S0894-0347-08-00593-6

has been cited by the following article:

• TITLE: Uniform Lipschitz Bound for a Competition Diffusion Advection System with Strong Competition

  AUTHORS: Tingwei Huang, Shan Zhang

  KEYWORDS: Diffusion-Advection System, Free Boundary Problem, Uniform Lipschitz Bound

  JOURNAL NAME: Applied Mathematics, Vol.12 No.5, May 19, 2021

  ABSTRACT: We prove the uniform Lipschitz bound of solutions for a nonlinear elliptic system modeling the steady state of populations that compete in a heterogeneous environment. This extends known quasi-optimal regularity results and covers the optimal case for this problem. The proof relies upon the blow-up technique and the almost monotonicity formula by Caffarelli, Jerison and Kenig.