{"id":{"repo_id":"qucosa-diss","oai_identifier":"oai:qucosa:de:qucosa:23627"},"canonical_url":"https://search.dev.ndltd.org/etd/qucosa-diss/oai:qucosa:de:qucosa:23627","repository":{"repo_id":"qucosa-diss","name":"QUCOSA","base_url":"http://www.qucosa.de/oai/"},"display":{"title":"Eigenvalue Problem for the 1-Laplace Operator","abstract":"We consider the eigenvalue problem associated to the 1-Laplace operator. We define higher eigensolutions by means of weak slope and establish existence of a sequence of eigensolutions by using nonsmooth critical point theory. In addition, we deduce a new necessary condition for the first eigenvalue of the 1-Laplace operator by means of inner variations.","abstract_html":"We consider the eigenvalue problem associated to the 1-Laplace operator. We define higher eigensolutions by means of weak slope and establish existence of a sequence of eigensolutions by using nonsmooth critical point theory. In addition, we deduce a new necessary condition for the first eigenvalue of the 1-Laplace operator by means of inner variations.","abstract_has_math":false,"creators":["Milbers, Zoja"],"institution":"Technische Universität Dresden","degree_name":null,"degree_level":"thesis.doctoral","degree_discipline":null,"degree_department":null,"school":null,"contributors":["Schuricht, Friedemann","Kawohl, Bernd","Degiovanni, Marco"],"advisors":[],"committee_chairs":[],"committee_members":[],"year":2009,"date_issued":"2009-03-23","date_published":"2009-03-23","updated_at":"2026-07-24T03:57:28Z","subjects":["1-Laplace","nonsmooth critical point theory","weak slope","inner variations","nichtglatte Theorie kritischer Punkte","innere Variationen"],"languages":[],"rights":[],"rights_urls":[],"identifier_entries":[]},"links":{"outbound_url":null,"outbound_label":null,"outbound_source":null},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor","label":"Contributor","values":["Schuricht, Friedemann","Kawohl, Bernd","Degiovanni, Marco"]},{"key":"dc:creator","label":"Author","values":["Milbers, Zoja"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:publisher","label":"Institution","values":["Saechsische Landesbibliothek- Staats- und Universitaetsbibliothek Dresden","Technische Universität Dresden"]},{"key":"dc:type","label":"Dc Type","values":["doctoralThesis"]},{"key":"thesis:degree_level","label":"Degree Level","values":["thesis.doctoral"]},{"key":"thesis:institution_name","label":"Thesis Institution Name","values":["Technische Universität Dresden"]}]},{"id":"subjects_keywords","label":"Subjects and Keywords","entries":[{"key":"dc:subject","label":"Dc Subject","values":["1-Laplace","nonsmooth critical point theory","weak slope","inner variations","nichtglatte Theorie kritischer Punkte","innere Variationen"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description.abstract","label":"Abstract","values":["We consider the eigenvalue problem associated to the 1-Laplace operator. We define higher eigensolutions by means of weak slope and establish existence of a sequence of eigensolutions by using nonsmooth critical point theory. In addition, we deduce a new necessary condition for the first eigenvalue of the 1-Laplace operator by means of inner variations.","Wir betrachten das zum 1-Laplace-Operator gehörige Eigenwertproblem. Wir definieren höhere Eigenlösungen mittels weak slope und weisen die Existenz einer Folge von Eigenlösungen nach, indem wir die nichtglatte Theorie kritischer Punkte anwenden. Zusätzlich leiten wir eine neue notwendige Bedingung für den ersten Eigenwert des 1-Laplace-Operators mittels innerer Variationen her."]},{"key":"dc:title","label":"Title","values":["Eigenvalue Problem for the 1-Laplace Operator"]}]}],"canonical_facts":{"dc:contributor":["Schuricht, Friedemann","Kawohl, Bernd","Degiovanni, Marco"],"dc:creator":["Milbers, Zoja"],"dc:description.abstract":["We consider the eigenvalue problem associated to the 1-Laplace operator. We define higher eigensolutions by means of weak slope and establish existence of a sequence of eigensolutions by using nonsmooth critical point theory. In addition, we deduce a new necessary condition for the first eigenvalue of the 1-Laplace operator by means of inner variations.","Wir betrachten das zum 1-Laplace-Operator gehörige Eigenwertproblem. Wir definieren höhere Eigenlösungen mittels weak slope und weisen die Existenz einer Folge von Eigenlösungen nach, indem wir die nichtglatte Theorie kritischer Punkte anwenden. Zusätzlich leiten wir eine neue notwendige Bedingung für den ersten Eigenwert des 1-Laplace-Operators mittels innerer Variationen her."],"dc:publisher":["Saechsische Landesbibliothek- Staats- und Universitaetsbibliothek Dresden","Technische Universität Dresden"],"dc:subject":["1-Laplace","nonsmooth critical point theory","weak slope","inner variations","nichtglatte Theorie kritischer Punkte","innere Variationen"],"dc:title":["Eigenvalue Problem for the 1-Laplace Operator"],"dc:type":["doctoralThesis"],"thesis:degree_level":["thesis.doctoral"],"thesis:institution_name":["Technische Universität Dresden"]},"updated_at":"2026-07-24T03:57:28Z"}