| الملخص: | This article deals with elliptic systems of the form −∑i=1n∂∂xi∑β=1N∑j=1nai,jα,β(x,u(x))∂uβ(x)∂xj=fα(x),α=1,…,N.-\mathop{\sum }\limits_{i=1}^{n}\frac{\partial }{\partial {x}_{i}}\left(\mathop{\sum }\limits_{\beta =1}^{N}\mathop{\sum }\limits_{j=1}^{n}{a}_{i,j}^{\alpha ,\beta }\left(x,u\left(x))\frac{\partial {u}^{\beta }\left(x)}{\partial {x}_{j}}\right)={f}^{\alpha }\left(x),\hspace{1em}\alpha =1,\ldots ,N. Under ellipticity conditions of the diagonal coefficients and proportional conditions of the off-diagonal coefficients, we derive local and global boundedness results. Under ellipticity of all the coefficients and “butterfly” support of off-diagonal coefficients, we derive a global boundedness result. This article also considers regularizing effect of a lower-order term.
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