Geodesic
Hölder continuity of bounded generalized solutions for some degenerated quasilinear elliptic equations with natural growth terms
Commentationes Mathematicae Universitatis Carolinae, Tome 59 (2018) no. 1, pp. 45-64.

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We prove the local Hölder continuity of bounded generalized solutions of the Dirichlet problem associated to the equation $\sum_{i =1}^{m} \frac{\partial}{\partial x_i} a_i (x, u, \nabla u) - c_0 |u|^{p-2} u = f(x, u, \nabla u),$ assuming that the principal part of the equation satisfies the following degenerate ellipticity condition $\lambda (|u|) \sum_{i=1}^m a_i (x,u, \eta) \eta_i \geq \nu(x) |\eta|^p,$ and the lower-order term $f$ has a natural growth with respect to $\nabla u$.
DOI : 10.14712/1213-7243.2015.242
Classification : 35B65, 35J15, 35J70
Keywords: elliptic equations; weight function; regularity of solutions 
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Bonafede, Salvatore. Hölder continuity of bounded generalized solutions for some degenerated quasilinear elliptic equations with natural growth terms. Commentationes Mathematicae Universitatis Carolinae, Tome 59 (2018) no. 1, pp. 45-64. doi : 10.14712/1213-7243.2015.242. http://geodesic.mathdoc.fr/articles/10.14712/1213-7243.2015.242/

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