Existence and global Holder continuity are proved for the weak solution to the Dirichlet problem {div(a(ij)(x, u)D(j)u + a(t)(x, u)) = b(x, u, Du) in Omega subset of R(n), u = 0 on partial derivative Omega over Reifenberg flat domains Omega. The principal coefficients a(ij)(x, u) are discontinuous with respect to x with small BMO-norms and b(x, u, Du) grows as vertical bar Du vertical bar(r) with r < 1 + 2/n.
Quasilinear divergence form elliptic equations in rough domains / Palagachev, Dian Kostadinov. - In: COMPLEX VARIABLES AND ELLIPTIC EQUATIONS. - ISSN 1747-6933. - STAMPA. - 55:5-6(2010), pp. 581-591. [10.1080/17476930903276159]
Quasilinear divergence form elliptic equations in rough domains
Dian Kostadinov Palagachev
2010-01-01
Abstract
Existence and global Holder continuity are proved for the weak solution to the Dirichlet problem {div(a(ij)(x, u)D(j)u + a(t)(x, u)) = b(x, u, Du) in Omega subset of R(n), u = 0 on partial derivative Omega over Reifenberg flat domains Omega. The principal coefficients a(ij)(x, u) are discontinuous with respect to x with small BMO-norms and b(x, u, Du) grows as vertical bar Du vertical bar(r) with r < 1 + 2/n.File in questo prodotto:
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