We consider a class of nonlinear elliptic problems whose prototype involves a coefficients matrix blowing up for a finite value m of the unknown u. Since datum is in \(L^1\), a suitable notion of renormalized solutions is introduced taking into account that u can reach the value m and the existence of such solutions is proved. We study the corresponding evolution problem as well.

中文翻译：

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具有无界系数和$$ L ^ 1 $$ L 1数据的非线性问题

我们考虑一类非线性椭圆问题，其原型涉及系数矩阵，该矩阵爆炸了未知u的有限值m。由于数据位于\（L ^ 1 \）中，因此考虑到u可以达到m值，引入了合适的重归一化解的概念，并证明了此类解的存在性。我们也研究相应的演化问题。