[Dottorcomp] Seminari di Matematica Applicata, 19/05/2026, Alessandra De Luca

[Stefano Lisini]

Seminari di Matematica Applicata, Dipartimento di Matematica "F. Casorati"
e Istituto del CNR IMATI "E. Magenes" di Pavia.

Martedì 19 Maggio 2026, alle *ore 15* precise, presso l'aula Beltrami del
Dipartimento di Matematica,

Alessandra De Luca (Università di Milano Bicocca)

terrà un seminario dal titolo:

Unique continuation from the boundary for the spectral fractional Laplacian.

Abstract: After a brief introduction to the unique continuation principle,
I will discuss its validity at the boundary for a class of nonlocal
elliptic equations driven by the spectral fractional Laplacian (−Δ𝐷)𝑠,
defined via fractional powers of the Dirichlet eigenvalues.
More precisely, an extension procedure allows to reduce the problem to a
local equation in one higher dimension, posed on a cylinder with a
homogeneous Dirichlet condition on the lateral boundary and a
non-homogeneous Neumann condition on the base.
For the extended problem, after an odd reflection across the junction
between the basis and the lateral surface of the cylinder, enough
regularity is available to derive a Pohozaev-type identity and consequently
some doubling properties via an Almgren-type monotonicity formula.
Combining this with a blow-up analysis, which gives information on all the
admissible vanishing orders of solutions, we get the strong unique
continuation property for the nonlocal problem.
Finally, I will also present a new project concerning the Neumann spectral
fractional Laplacian (−Δ𝑁)𝑠.

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https://matematica.unipv.it/ricerca/cicli-di-seminari/seminari-di-matematica-applicata/