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
2018-01-01

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$.
2018
elliptic equations; weight function; regularity of solutions
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/20.500.12318/2921
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