A Local estimate for nonlinear equations with discontinuous coefficients
A Local estimate for nonlinear equations with discontinuous coefficients
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DOI：
10.1080/03605309908821494
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发表时间：
1999
影响因子：
1.9
通讯作者：
J. Kinnunen;Shulin Zhou
中科院分区：
文献类型：
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作者：
J. Kinnunen;Shulin Zhou
2044 KINNUNEN AND ZHOU for all (E Rn and almost every x E Q. Here X and A are posit, ive constants and q.(denotes the standard inner product of v, Je Rn. Suppose that F E L~,,(J?). We secali that the function u E w,::(R) is a weak solution for equation (1.1) if for every p E Cr (f2). Equation (1.1) arises naturally in many different contexts. Just to mention few, we point out that it is the Euler equation for the variational integralIn the case p= n equation (1.1)(with F= 0) plays a key role in theory of quasiconformal mappings. If A is the identity matrix, then we have a non-homogeneous p-harmonic equation. We are interested in studying how the regularity of F is reflected to the solutions under minimal assumptions on the coefficient matrix A. In particular, we are keen on having discontinuous coefficients. A natural weakening of the case with smooth coefficients is to assume that the coefficients of the matrix A are of vanishing mean oscillation. We recall that a locally integrable function f is of bounded mean oscillation, if
