REGULARITY FOR SOLUTIONS TO NONHOMOGENEOUS QUASILINEAR ELLIPTIC SYSTEMS*
GAO HONGYA *
College of Mathematics and Information Science, Hebei University, Baoding, 071002, China
CUI YI
College of Mathematics and Information Science, Hebei University, Baoding, 071002, China
LIAGN SHUANG
College of Mathematics and Information Science, Hebei University, Baoding, 071002, China
*Author to whom correspondence should be addressed.
Abstract
In the present paper we consider regularity properties for weak solutions u: Ω ⊂ Rn → RN of nonhomogeneous quasilinear elliptic systems of the form
The diagonal coefficients aγγij (x,y) are elliptic for large values of yγ (the γ-th component of y = (y1, ..., yN)), the off-diagonal coefficients are small when every component yγ is large: there exists θγ > 0 and q > 0 such that
Furthermore,
Under the previous assumptions, we derive u ∈ L2∗(1+q)weak(Ω,RN) for every weak solution u ∈ W1,2(Ω,RN) of (∗).
Keywords: Integrability, weak solution, nonhomogeneous quasilinear elliptic system