{"id":{"repo_id":"cagliari","oai_identifier":"oai:iris.unica.it:11584/266589"},"canonical_url":"https://search.dev.ndltd.org/etd/cagliari/oai:iris.unica.it:11584/266589","repository":{"repo_id":"cagliari","name":"Università di Cagliari","base_url":"https://iris.unica.it/oai/request"},"display":{"title":"On two problems related to the Laplace operator","abstract":"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.","abstract_html":"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.","abstract_has_math":false,"creators":["FARINA, MARIA ANTONIETTA"],"institution":"Università degli Studi di Cagliari","degree_name":null,"degree_level":null,"degree_discipline":null,"degree_department":null,"school":null,"contributors":[],"advisors":[],"committee_chairs":[],"committee_members":[],"year":2015,"date_issued":"2015-04-16","date_published":"2015-04-16","updated_at":"2026-07-24T01:30:07Z","subjects":["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"],"languages":["eng"],"rights":["info:eu-repo/semantics/openAccess","license:Non specificato"],"rights_urls":[],"identifier_entries":[]},"links":{"outbound_url":"http://hdl.handle.net/11584/266589","outbound_label":"Handle","outbound_source":"dc:identifier"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:creator","label":"Author","values":["FARINA, MARIA ANTONIETTA"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date","label":"Dc Date","values":["2015-04-16"]},{"key":"dc:publisher","label":"Institution","values":["Università degli Studi di Cagliari"]},{"key":"dc:relation","label":"Dc Relation","values":["numberofpages:76"]},{"key":"dc:type","label":"Dc Type","values":["info:eu-repo/semantics/doctoralThesis"]}]},{"id":"subjects_keywords","label":"Subjects and Keywords","entries":[{"key":"dc:subject","label":"Dc Subject","values":["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"]}]},{"id":"language_rights","label":"Language and Rights","entries":[{"key":"dc:language","label":"Dc Language","values":["eng"]},{"key":"dc:rights","label":"Dc Rights","values":["info:eu-repo/semantics/openAccess","license:Non specificato"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier","label":"Identifier","values":["http://hdl.handle.net/11584/266589"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description","label":"Description","values":["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."]},{"key":"dc:title","label":"Title","values":["On two problems related to the Laplace operator"]}]}],"canonical_facts":{"dc:creator":["FARINA, MARIA ANTONIETTA"],"dc:date":["2015-04-16"],"dc:description":["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."],"dc:identifier":["http://hdl.handle.net/11584/266589"],"dc:language":["eng"],"dc:publisher":["Università degli Studi di Cagliari"],"dc:relation":["numberofpages:76"],"dc:rights":["info:eu-repo/semantics/openAccess","license:Non specificato"],"dc:subject":["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"],"dc:title":["On two problems related to the Laplace operator"],"dc:type":["info:eu-repo/semantics/doctoralThesis"]},"updated_at":"2026-07-24T01:30:07Z"}