TITLE:
Regularity Theory for Elliptic Equations with Anisotropic Diffusion
AUTHORS:
Mengru Liu, Ling Zhou
KEYWORDS:
Anisotropic Diffusion, Blow-Up, Strongly Competitive Elliptic Systems, Regularity of Weak Solutions
JOURNAL NAME:
Journal of Applied Mathematics and Physics,
Vol.14 No.4,
April
15,
2026
ABSTRACT: For a class of strongly competitive elliptic systems with anisotropic diffusion posed on an open set
Ω⊂
ℝ
N
(
N≥3
)
, we establish regularity estimates for weak solutions by a contradiction argument, via the construction of blow-up sequences and the use of monotonicity formulas together with Liouville-type theorems.