We prove the localH"older continuity of bounded generalized solutions of theDirichlet problem associated to the equation$$ qquadqquaddisplaystyle{sum_{i =1}^{m} rac{partial}{partial x_i} a_i (x, u, abla u)- c_0 |u|^{p-2} u = f(x, u, abla u)},$$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 $ abla u$.

Hölder continuity of bounded generalized solutions for some degenerated quasilinear elliptic equations with natural growth terms.

BONAFEDE, Salvatore
2018

Abstract

We prove the localH"older continuity of bounded generalized solutions of theDirichlet problem associated to the equation$$ qquadqquaddisplaystyle{sum_{i =1}^{m} rac{partial}{partial x_i} a_i (x, u, abla u)- c_0 |u|^{p-2} u = f(x, u, abla u)},$$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 $ abla u$.
elliptic equations; weight function; regularity of solutions
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/20.500.12318/2921
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