2026-09-23T00:54:45Zhttps://iris.unica.it/oai/requestoai:iris.unica.it:11584/2665892022-10-17T14:17:39Zcom_11584_207615com_11584_111066col_11584_265854
On two problems related to the Laplace operator
FARINA, MARIA ANTONIETTA
autovalore principale
brownian motion
coarea formula
dinamica delle popolazioni
dominio armonico
formula della coarea
harmonic domain
massimizzazione
maximization
minimization
minimizzazione
moto browniano
population dynamics
principal eigenvalue
rearrangements
riordinamenti
rottura della simmetria
symmetry breaking
Settore MAT/03 - Geometria
We investigate maximization of the functional Ω → ε(Ω) where Ω runs in the set
of compact domains of fixed volume v in any Riemannian manifold (M; g) and
where ε(Ω) is the mean exit time from
of the Brownian motion. Concerning
this functional, we study its critical points and prove that they are harmonic
domains. We analyze the special case of the Coarea formula when we take a
Morse function. We investigate minimization and maximization of the principal
eigenvalue of the Laplacian under mixed boundary conditions in case the weight
has indefinite sign and varies in the class of rearrangements of a fixed function
g0 defined on a smooth and bounded domain Ω
in Rn. We prove existence
and uniqueness results, and in special cases, we prove results of symmetry and
results of symmetry breaking for the minimizer.
2015-04-16
info:eu-repo/semantics/doctoralThesis
http://hdl.handle.net/11584/266589
eng
numberofpages:76
info:eu-repo/semantics/openAccess
Università degli Studi di Cagliari
license:Non specificato