Hopf’s lemmas and boundary point results for the fractional p-Laplacian.

Abstract: In this talk, we will discuss  different versions of the classical Hopf’s boundary lemma in the setting of the fractional $p-$Laplacian, for $p \geq 2$. We will start with a  Hopf’s lemma   based on comparison principles and for  constant-sign potentials. Afterwards, we will present a Hopf’s result for sign-changing potentials describing the behavior of the fractional normal derivative of solutions around boundary points. As we wiil see, the main contribution here is that we do not need to impose a global condition on the sign of the solution. Applications of the main results to boundary point lemmas and a discussion of  non-local non-linear overdetermined problems will also be discussed.

Posted on Sep 27, 2024 in Differential Equations, Seminars