Virtual Talk: Eigenvalue estimates for p-Laplace problems on domains expressed in Fermi Coordinates

Barbara Brandolini
Università degli Studi di Palermo

We prove explicit and sharp eigenvalue estimates for Neumann p-Laplace
eigenvalues in domains that admit a representation in Fermi coordinates. More precisely, if
? denotes a non-closed curve in R
symmetric with respect to the y-axis, let D ? R
2 denote
the domain of points that lie on one side of ? and within a prescribed distance d(s) from
?(s) (here s denotes the arc length parameter for ?). Write µ
(D) for the lowest nonzero
eigenvalue of the Neumann p-Laplacian with an eigenfunction that is odd with respect to
the y-axis. For all p > 1, we provide a lower bound on µ
(D) when the distance function
d and the signed curvature k of ? satisfy certain geometric constraints. In the linear case
(p = 2), we establish sufficient conditions to guarantee µ
(D) = µ1(D).
This is a joint work with F. Chiacchio and J. J. Langford.

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