Mathematica Eterna
Open Access

Abstract

Integrability for Solutions to Some Nonhomogeneous Quasilinear Elliptic Problems

Miaomiao JIA and Jiapeng YANG

In this paper we prove an estimate for the measure of superlevel sets for weak solutions u of nonhomogeneous quasilinear elliptic systems − Xn i=1 Di   Xn j=1 X N β=1 a αβ ij (x, u(x))Dju β (x)   = − Xn i=1 Dif α i (x, u(x)), (∗) α = 1, 2, · · · , N. The diagonal coefficients a γγ ij (x, y) are elliptic for large values of u, the off-diagonal coefficients are small when |u| is large, the faster offdiagonal coefficients decay, the higher integrability of u becomes.