Quasi-linear degenerate elliptic problems with \(L^1\) data. (English) Zbl 1274.35108
Summary: We prove existence and uniqueness of a solution for a class of quasi-linear problems with \(L^1\) data. The diffusion matrix \(\mathbf A(x,u)\) is allowed to degenerate with respect to the unknown \(u\). We obtain uniqueness of the solution under a weak assumption on \(\mathbf A(x,u)\) that permits to consider highly oscillating or/and increasing coefficients (with respect to \(u\)).
MSC:
| 35J60 | Nonlinear elliptic equations |
| 35J70 | Degenerate elliptic equations |
| 35R05 | PDEs with low regular coefficients and/or low regular data |
References:
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