Estimates in the generalized Campanato-John-Nirenberg spaces for fully nonlinear elliptic equations. (English) Zbl 1039.35034

Caffarelli, Luis A.; Huang, Qingbo

Duke Math. J. 118, No. 1, 1-17 (2003).

The authors consider estimates in the generalized Campanato-John-Nirenberg spaces \(\text{BMO}_\Psi\) for solutions to the fully nonlinear elliptic equation \(F(x, D^2u)= f(x),\) where \(\Omega\) is a bounded domain in \(\mathbb{R}^N\). To obtain \(\text{BMO}_\Psi\)-estimates the authors use a perturbation argument and first prove that the Evans-Krylov estimates imply Campanato inequalities.

Reviewer: Messoud A. Efendiev (Berlin)

MSC:

35J60	Nonlinear elliptic equations
35B65	Smoothness and regularity of solutions to PDEs

Keywords:

Campanato-John-Nirenberg space; Evans-Krylov estimate; nonlinear elliptic equation

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