{"id":"https://openalex.org/keywords/neumann-problem","display_name":"Neumann problem","description":"A boundary-value problem for a differential equation in which the normal derivative of the solution is specified along the domain boundary.","display_name_alternatives":["Neumann boundary value problem","Neumann problems","second boundary value problem"],"ids":{"openalex":"https://openalex.org/keywords/neumann-problem","wikidata":"https://www.wikidata.org/wiki/Q1149279"},"primary_topic":{"id":"https://openalex.org/T12589","display_name":"Differential Equations and Boundary Problems","score":0.2397,"subfield":{"id":"https://openalex.org/subfields/2604","display_name":"Applied Mathematics"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T12589","display_name":"Differential Equations and Boundary Problems","score":0.2397,"subfield":{"id":"https://openalex.org/subfields/2604","display_name":"Applied Mathematics"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10194","display_name":"Nonlinear Partial Differential Equations","score":0.2266,"subfield":{"id":"https://openalex.org/subfields/2604","display_name":"Applied Mathematics"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"works_count":5134,"cited_by_count":77458,"works_api_url":"https://api.openalex.org/works?filter=keywords.id:keywords/neumann-problem","updated_date":"2026-10-23T04:06:34","created_date":"2026-09-30T00:00:00"}
