Year: 2025
Type: preprint
Abstract: We consider general nonlinear elliptic equations of the form \[ \operatorname{div}\, A(x,Du) = 0 \quad \text{in } Ω, \] where $A:Ω\times \mathbb R^n \to \mathbb R^n$ satisfies a quasi-isotropic $(p,q)$-growth condition, which is equivalent to the point-wise uniform ellipticity of $A$. We establish sharp and comprehensive mean oscillation conditions on $A(x,ξ)$ with respect to the $x$ variable to obtain $C^1$- and $W^{1,s}$-regularity results. The results provide new conditions even in the standard $p$-growth case with coefficient $\operatorname{div}(a(x)|Du|^{p-2}Du)=0$. Also included are variable exponent growth with and without perturbation as well as borderline double-phase growth and double-phase growth with a coefficient.
Source: arXiv (Cornell University)
Authors: Hästö, Peter, Lee, Mikyoung, Ok, Jihoon
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W4409696756