Partial regularity of solutions of fully nonlinear, uniformly elliptic equations
By S. Armstrong, Luis Silvestre, Charles K. Smart. 2011
60 citations recorded by the source corpus.
We prove that a viscosity solution of a uniformly elliptic, fully nonlinear equation is C2,α on the complement of a closed set of Hausdorff dimension at most ϵ less than the dimension. The equation is assumed to be C1, and the constant ϵ > 0 depends only on the dimension and the ellipticity constants. The argument combines the W2,ϵ estimates of Lin with a result of Savin on the C2,α regularity of viscosity solutions that are close to quadratic polynomials. © 2012 Wiley Periodicals, Inc.
Subfields: Applied Mathematics, Computational Theory and Mathematics
View Paper: https://www.semanticscholar.org/paper/8002347dfe67900a88ce9a6b318ca93cd3f531da
How researchers see this paper
The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.
In Applied Mathematics
- Charles K. Smart
- S. Armstrong
- Zhongwei Shen
- Jean-Christophe Mourrat
- Tuomo Kuusi
- Nikos Katzourakis
- Felix Otto
In Computational Theory and Mathematics
- S. Armstrong
- Charles K. Smart
- Zhongwei Shen
- Jean-Christophe Mourrat
- Tuomo Kuusi
- Felix Otto
- Antoine Gloria
- Stefan Neukamm
Citations in the corpus
- Quantitative Stochastic Homogenization of Elliptic Equations in Nondivergence Form (2013, methodology): “However, the estimates from [1] (Proposition 3.”