On the smoothness of solutions of fully nonlinear second order equations in the plane
Abstract
Abstract We study interior $$C^{2,\alpha }$$ C 2 , α regularity estimates for solutions of fully nonlinear uniformly elliptic equations of the general form $$F(D^2u)=0$$ F ( D 2 u ) = 0 in two independent variables and without any geometric condition on F . By means of the theory of divergence form equations we prove that $$C^2$$ C 2 solutions of the previous equation are $$C^{2,\bar{\alpha }(\lambda /\Lambda )}$$ C 2 , α ¯ ( λ / Λ ) in the interior of the domain, where $$0\lambda /\Lambda $$ α ~ = α ~ ( λ / Λ ) > λ / Λ .
Fields of Study & Subjects
Nonlinear Partial Differential Equations
Advanced Harmonic Analysis Research
Numerical methods in inverse problems
Publication details
- Journal / source
- Partial Differential Equations and Applications
- Publisher
- Springer Science and Business Media LLC
- Volume
- 7
- Issue
- 1
- Publication date
- 18 February 2026
- Language
- EN