| Abstract: |
| We will present recent advances in the study of nonlinear systems. The main challenge in dealing with those systems is the lack of comparison principle and of the classical Perron`s method. Nevertheless, we discover a chain reaction, exploiting the properties of an equation along the system and obtaining higher sharp regularity across the free boundary. Additionally, we prove geometric measure estimates and obtain coincidence of the free boundaries. Furthermore, we derive free boundary regularly results. These results are new, even for linear systems. |
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