## Salvatore Bonafede

*H\"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

PDF