\(C^{1+\alpha}\) local regularity of weak solutions of degenerate elliptic equations. (English) Zbl 0539.35027

From the author’s introduction: ”The main result of this paper is the \(C^{1+\alpha}\) nature of local weak solutions of elliptic equations of the type \[ (1.1)\quad -div \vec a(x,u,\nabla u)+b(x,u,\nabla u)=0\quad in\quad {\mathcal D}'(\Omega) \] where \(\Omega\) is an open set in \({\mathbb{R}}^ N\), \(N\geq 2\), \(\vec a\) is a map from \({\mathbb{R}}^{2N+1}\) into \({\mathbb{R}}^ N\) and b maps \({\mathbb{R}}^{2N+1}\) into \({\mathbb{R}}\). The point here is that we do not assume uniform ellipticity of the leading part of (1.1), which is allowed to be degenerate for certain values of \(| \nabla u|.''\)
Reviewer: M.Chicco


35J60 Nonlinear elliptic equations
35B65 Smoothness and regularity of solutions to PDEs
35J70 Degenerate elliptic equations
35J15 Second-order elliptic equations
35D10 Regularity of generalized solutions of PDE (MSC2000)
Full Text: DOI


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