Regularity for a fourth-order critical equation with gradient nonlinearity

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:369

Article

Fabbri, Isabella

关键词: Biharmonic equation;    Gradient nonlinearity;    Regularity;   

DOI  :  10.1016/j.jmaa.2010.02.040

来源: Elsevier

【 摘 要 】

Given Omega a smooth bounded domain of R(n), n >= 3, we consider functions u is an element of H(2.0)(2)(Omega) that are weak solutions to the equation Delta(2)u + au = -div(f/vertical bar x vertical bar(s)vertical bar del u vertical bar(2)*(-2)del u) in Omega, where 2* := 2(n-s)/n-2, S is an element of [0,2) and a, f is an element of C(infinity)((Omega) over bar )In this article, we prove the maximal regularity of solutions to the above equation, depending on the value of s is an element of [0,2) and the relative position of Omega with respect to the origin. In particular, the solutions are in C(4)((Omega) over bar) when s = 0. (C) 2010 Elsevier Inc. All rights reserved.

【 授权许可】

Free