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Zbl 0539.35027
DiBenedetto, E.
$C\sp{1+\alpha}$ local regularity of weak solutions of degenerate elliptic equations.
(English)
[J] Nonlinear Anal., Theory Methods Appl. 7, 827-850 (1983). ISSN 0362-546X

From the author's introduction: "The main result of this paper is the $C\sp{1+\alpha}$ nature of local weak solutions of elliptic equations of the type $$(1.1)\quad -div \vec a(x,u,\nabla u)+b(x,u,\nabla u)=0\quad in\quad {\cal D}'(\Omega)$$ where $\Omega$ is an open set in ${\bbfR}\sp N$, $N\ge 2$, $\vec a$ is a map from ${\bbfR}\sp{2N+1}$ into ${\bbfR}\sp N$ and b maps ${\bbfR}\sp{2N+1}$ into ${\bbfR}$. 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 $\vert \nabla u\vert.''$
[M.Chicco]
MSC 2000:
*35J60 Nonlinear elliptic equations
35B65 Smoothness of solutions of PDE
35J70 Elliptic equations of degenerate type
35J15 Second order elliptic equations, general
35D10 Regularity of generalized solutions of PDE

Keywords: singular equations; quasilinear elliptic equations; local regularity; local weak solutions

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