{"id":{"repo_id":"umn","oai_identifier":"oai:conservancy.umn.edu:11299/141670"},"canonical_url":"https://search.dev.ndltd.org/etd/umn/oai:conservancy.umn.edu:11299/141670","repository":{"repo_id":"umn","name":"University of Minnesota","base_url":"https://conservancy.umn.edu/server/oai/request"},"display":{"title":"Error estimates for finite difference solutions of second-order elliptic equations in discrete Sobolev spaces","abstract":"We derive a priori lp-estimates for nite difference solutions of second-order elliptic equations with continuous coefficients in the whole space. We shall mainly use the Fefferman-Stein theorem and discrete Sobolev inequalities to establish our purpose. Based on these lp-estimates, we obtain the convergence rate of the approximate solutions and their difference quotients in the sup norm.","abstract_html":"We derive a priori lp-estimates for nite difference solutions of second-order elliptic equations with continuous coefficients in the whole space. We shall mainly use the Fefferman-Stein theorem and discrete Sobolev inequalities to establish our purpose. Based on these lp-estimates, we obtain the convergence rate of the approximate solutions and their difference quotients in the sup norm.","abstract_has_math":false,"creators":["Doh, Hyun Soo"],"institution":null,"degree_name":null,"degree_level":null,"degree_discipline":null,"degree_department":null,"school":null,"contributors":[],"advisors":[],"committee_chairs":[],"committee_members":[],"year":2012,"date_issued":"2012-08","date_published":"2012-08","updated_at":"2026-07-24T05:20:07Z","subjects":["Finite difference approximations","lp error estimates"],"languages":["en_US"],"rights":[],"rights_urls":[],"identifier_entries":[]},"links":{"outbound_url":"http://purl.umn.edu/141670","outbound_label":"Repository record","outbound_source":"dc:identifier.uri"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:creator","label":"Author","values":["Doh, Hyun Soo"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date.accessioned","label":"Dc Date Accessioned","values":["2012-12-21T16:18:50Z"]},{"key":"dc:date.available","label":"Dc Date Available","values":["2012-12-21T16:18:50Z"]},{"key":"dc:date.issued","label":"Date","values":["2012-08"]},{"key":"dc:type","label":"Dc Type","values":["Thesis or Dissertation"]}]},{"id":"subjects_keywords","label":"Subjects and Keywords","entries":[{"key":"dc:subject","label":"Dc Subject","values":["Finite difference approximations","lp error estimates"]}]},{"id":"language_rights","label":"Language and Rights","entries":[{"key":"dc:language.iso","label":"Language (ISO)","values":["en_US"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier.uri","label":"Identifier URI","values":["http://purl.umn.edu/141670"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description","label":"Description","values":["University of Minnesota Ph.D. dissertatation. August 2012. Major:Mathematics. Advisor: Nicolai V. Krylov. 1 computer file (PDF); ii, 60 pages."]},{"key":"dc:description.abstract","label":"Abstract","values":["We derive a priori lp-estimates for nite difference solutions of second-order elliptic equations with continuous coefficients in the whole space. We shall mainly use the Fefferman-Stein theorem and discrete Sobolev inequalities to establish our purpose. Based on these lp-estimates, we obtain the convergence rate of the approximate solutions and their difference quotients in the sup norm."]},{"key":"dc:title","label":"Title","values":["Error estimates for finite difference solutions of second-order elliptic equations in discrete Sobolev spaces"]}]}],"canonical_facts":{"dc:creator":["Doh, Hyun Soo"],"dc:date.accessioned":["2012-12-21T16:18:50Z"],"dc:date.available":["2012-12-21T16:18:50Z"],"dc:date.issued":["2012-08"],"dc:description":["University of Minnesota Ph.D. dissertatation. August 2012. Major:Mathematics. Advisor: Nicolai V. Krylov. 1 computer file (PDF); ii, 60 pages."],"dc:description.abstract":["We derive a priori lp-estimates for nite difference solutions of second-order elliptic equations with continuous coefficients in the whole space. We shall mainly use the Fefferman-Stein theorem and discrete Sobolev inequalities to establish our purpose. Based on these lp-estimates, we obtain the convergence rate of the approximate solutions and their difference quotients in the sup norm."],"dc:identifier.uri":["http://purl.umn.edu/141670"],"dc:language.iso":["en_US"],"dc:subject":["Finite difference approximations","lp error estimates"],"dc:title":["Error estimates for finite difference solutions of second-order elliptic equations in discrete Sobolev spaces"],"dc:type":["Thesis or Dissertation"]},"updated_at":"2026-07-24T05:20:07Z"}