H'older continuity of bounded generalized solutions for some degenerated quasilinear elliptic equations with natural growth terms

摘要

We prove the local H"older continuity of bounded generalized solutions of the Dirichlet problem associated to the equation $$ sum_{i =1}^{m} rac{partial}{partial x_i} a_i (x, u, abla u) - c_0 |u|^{p-2} u = f(x, u, abla u), $$ assuming that the principal part of the equation satisfies the following degenerate ellipticity condition $$ lambda (|u|) sum_{i=1}^m a_i (x,u, eta) eta_i geq u(x) |eta|^p, $$ and the lower-order term $f$ has a natural growth with respect to $abla u$.