Juraj Húska
This talk will be accessible to anyone with basic pde knowledge. We will first review some basic properties of principal ("first") eigenvalues of elliptic operators. These come up in a variety of contexts when studying both linear and nonlinear elliptic and parabolic equations. We will then continue to explain how one can extend the notion of a principal eigenvalue to the context of linear nonautonomous parabolic equations. This generalization is not straightforward at all. We will see that new Harnack inequalities are of great help in this endeavor and they will help us answer a (to be seen) crucial question: do sign-changing solutions of parabolic equations (under suitable boundary conditions) grow slower than positive solutions? Most of this talk will be based on joint work with Peter Polacik and Mikhail Safonov.
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