| Abstract: |
| It is well known how the Maximum Principle (MP) in general fails to hold for uniformly elliptic operators of order higher than two, even in smooth convex domains. In D. Cassani and A. Tarsia (2022) it was shown in dimension two and three, by establishing a new Harnack type inequality with nonlocal remainder terms, that the validity of the positivity preserving property can be restored when lower order derivatives are taken into account as a perturbation of the higher order differential operator. We will present further advances in this direction, extending the validity of the MP to any dimension and fairly general domains. Moreover, we will discuss how the presence of inertial terms affects the range of the perturbation parameter, providing a balance between the positivity restoring effect of lower order derivatives and the mass energy. Applications to semilinear biharmonic equations are presented. |
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