$$C^{1+\alpha}$$ 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

MSC:

 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)
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References:

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