## Salvatore BonafedeH\"older continuity of bounded generalized solutions for some degenerated quasilinear elliptic equations with natural growth terms

Comment.Math.Univ.Carolin. 59,1 (2018) 45-64.

Abstract:We prove the local H\"older 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 $\nabla u$.

Keywords: elliptic equations; weight function; regularity of solutions

DOI: DOI 10.14712/1213-7243.2015.242
AMS Subject Classification: 35J15 35J70 35B65

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