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Crooks, E.C.M., Dancer, E.N. and Hilhorst, D. (2007) On Long-Time Dynamics for Competition-Diffusion Systems with Inhomogeneous Dirichlet Boundary Conditions. Topological Methods in Nonlinear Analysis, 30, 1-36.

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.