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Article

Bonafede, Salvatore
Hölder continuity of bounded generalized solutions for some degenerated quasilinear elliptic equations with natural growth terms. (English). Commentationes Mathematicae Universitatis Carolinae, vol. 59 (2018), issue 1, pp. 45-64
MSC: 35B65, 35J15, 35J70 | MR 3783808 | Zbl 06890396 | DOI: 10.14712/1213-7243.2015.242
Keywords:
elliptic equations; weight function; regularity of solutions
Summary:
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 $\nabla u$.
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