We prove existence and global Holder regularity of the weak solution to the Dirichlet problem {div (a(ij)(x, u)D(j)u) = b(x, u, Du) in Omega R(n), n >= 2, u = 0 on partial derivative Omega is an element of C(1). The coefficients a(ij)(x, u) are supposed to be VMO functions with respect to x while the term b(x, u, Du) allows controlled growth with respect to the gradient Du and satisfies a sort of sign-condition with respect to u. Our results correct and generalize the announcements in Ragusa (Nonlinear Differ Equ Appl 13: 605-617, 2007, Erratum in Nonlinear Differ Equ Appl 15: 277-277, 2008).
Discontinuous superlinear elliptic equations of divergence form / Palagachev, Dian Kostadinov. - In: NODEA-NONLINEAR DIFFERENTIAL EQUATIONS AND APPLICATIONS. - ISSN 1021-9722. - 16:6(2009), pp. 811-822. [10.1007/s00030-009-0036-7]
Discontinuous superlinear elliptic equations of divergence form
PALAGACHEV, Dian Kostadinov
2009-01-01
Abstract
We prove existence and global Holder regularity of the weak solution to the Dirichlet problem {div (a(ij)(x, u)D(j)u) = b(x, u, Du) in Omega R(n), n >= 2, u = 0 on partial derivative Omega is an element of C(1). The coefficients a(ij)(x, u) are supposed to be VMO functions with respect to x while the term b(x, u, Du) allows controlled growth with respect to the gradient Du and satisfies a sort of sign-condition with respect to u. Our results correct and generalize the announcements in Ragusa (Nonlinear Differ Equ Appl 13: 605-617, 2007, Erratum in Nonlinear Differ Equ Appl 15: 277-277, 2008).I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
