{"id":"https://openalex.org/W7220951871","doi":"https://doi.org/10.48550/arxiv.2610.09540","title":"Shortest Paths in Domains with Crack-Induced Constraints","display_name":"Shortest Paths in Domains with Crack-Induced Constraints","publication_year":2026,"publication_date":"2026-10-07","ids":{"openalex":"https://openalex.org/W7220951871","doi":"https://doi.org/10.48550/arxiv.2610.09540"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2610.09540","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.09540","pdf_url":"https://arxiv.org/pdf/2610.09540","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},"volume":null,"type":"preprint","is_traditional":true,"indexed_in":["arxiv","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/2610.09540","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5157959481","display_name":"Phiet Dau The","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I123565023","display_name":"Vietnam National University Ho Chi Minh City","ror":"https://ror.org/00waaqh38","country_code":"VN","type":"education","lineage":["https://openalex.org/I123565023"]},{"id":"https://openalex.org/I47265099","display_name":"Ho Chi Minh City University of Technology","ror":"https://ror.org/04qva2324","country_code":"VN","type":"education","lineage":["https://openalex.org/I123565023","https://openalex.org/I47265099"]}],"countries":["VN"],"is_corresponding":false,"raw_author_name":"The, Phiet Dau","raw_affiliation_strings":["Faculty of Applied Science , Ho Chi Minh City University of Technology (HCMUT) , 268 Ly Thuong Kiet , Dien Hong Ward , Ho Chi Minh City , Vietnam","Vietnam National University Ho Chi Minh City , Linh Xuan Ward , Ho Chi Minh City , Vietnam"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Faculty of Applied Science , Ho Chi Minh City University of Technology (HCMUT) , 268 Ly Thuong Kiet , Dien Hong Ward , Ho Chi Minh City , Vietnam","institution_ids":["https://openalex.org/I47265099"]},{"raw_affiliation_string":"Vietnam National University Ho Chi Minh City , Linh Xuan Ward , Ho Chi Minh City , Vietnam","institution_ids":["https://openalex.org/I123565023"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5157976346","display_name":"Phan Thanh An","orcid":null,"observed_orcids":[]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"An, Phan Thanh","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":null,"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10194","display_name":"Nonlinear Partial Differential Equations","score":0.5044000148773193,"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/T10194","display_name":"Nonlinear Partial Differential Equations","score":0.5044000148773193,"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/T10545","display_name":"Optimization and Variational Analysis","score":0.33640000224113464,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T12589","display_name":"Differential Equations and Boundary Problems","score":0.028300000354647636,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/shortest-path","display_name":"shortest path","score":0.7639999985694885},{"id":"https://openalex.org/keywords/hamilton-jacobi-equation","display_name":"Hamilton-Jacobi equation","score":0.9010000228881836},{"id":"https://openalex.org/keywords/state-constraints","display_name":"state constraints","score":0.8119999766349792},{"id":"https://openalex.org/keywords/cracks","display_name":"cracks","score":0.8399999737739563},{"id":"https://openalex.org/keywords/variational-inequalities","display_name":"variational inequalities","score":0.9539999961853027},{"id":"https://openalex.org/keywords/free-boundary","display_name":"free boundary","score":0.6140000224113464},{"id":"https://openalex.org/keywords/comparison-principle","display_name":"comparison principle","score":0.8220000267028809},{"id":"https://openalex.org/keywords/optimal-trajectories","display_name":"optimal trajectories","score":0.45500001311302185}],"concepts":[{"id":"https://openalex.org/C2777021972","wikidata":"https://www.wikidata.org/wiki/Q22976830","display_name":"Uniqueness","level":2,"score":0.7627000212669373},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6384999752044678},{"id":"https://openalex.org/C2776036281","wikidata":"https://www.wikidata.org/wiki/Q48769818","display_name":"Constraint (computer-aided design)","level":2,"score":0.5885000228881836},{"id":"https://openalex.org/C36503486","wikidata":"https://www.wikidata.org/wiki/Q11235244","display_name":"Domain (mathematical analysis)","level":2,"score":0.5404999852180481},{"id":"https://openalex.org/C161999928","wikidata":"https://www.wikidata.org/wiki/Q4556320","display_name":"Variational inequality","level":2,"score":0.48739999532699585},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.4645000100135803},{"id":"https://openalex.org/C59085676","wikidata":"https://www.wikidata.org/wiki/Q957852","display_name":"Fracture mechanics","level":2,"score":0.4625000059604645},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.4560999870300293},{"id":"https://openalex.org/C182310444","wikidata":"https://www.wikidata.org/wiki/Q1332643","display_name":"Boundary value problem","level":2,"score":0.44690001010894775},{"id":"https://openalex.org/C62354387","wikidata":"https://www.wikidata.org/wiki/Q875399","display_name":"Boundary (topology)","level":2,"score":0.44440001249313354},{"id":"https://openalex.org/C48103436","wikidata":"https://www.wikidata.org/wiki/Q599031","display_name":"State (computer science)","level":2,"score":0.3921000063419342},{"id":"https://openalex.org/C65682993","wikidata":"https://www.wikidata.org/wiki/Q1056451","display_name":"Reflection (computer programming)","level":2,"score":0.34310001134872437},{"id":"https://openalex.org/C9259290","wikidata":"https://www.wikidata.org/wiki/Q745215","display_name":"Variational principle","level":2,"score":0.30809998512268066},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.2858000099658966},{"id":"https://openalex.org/C129537906","wikidata":"https://www.wikidata.org/wiki/Q7603913","display_name":"State variable","level":2,"score":0.27090001106262207},{"id":"https://openalex.org/C2780841128","wikidata":"https://www.wikidata.org/wiki/Q5073781","display_name":"Characterization (materials science)","level":2,"score":0.26660001277923584},{"id":"https://openalex.org/C18762648","wikidata":"https://www.wikidata.org/wiki/Q42213","display_name":"Work (physics)","level":2,"score":0.26260000467300415},{"id":"https://openalex.org/C26955809","wikidata":"https://www.wikidata.org/wiki/Q10167591","display_name":"Initial value problem","level":2,"score":0.2606000006198883},{"id":"https://openalex.org/C155940","wikidata":"https://www.wikidata.org/wiki/Q7886967","display_name":"Uniqueness theorem for Poisson's equation","level":3,"score":0.2538999915122986},{"id":"https://openalex.org/C14646407","wikidata":"https://www.wikidata.org/wiki/Q1430750","display_name":"Bellman equation","level":2,"score":0.2533999979496002},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.25270000100135803}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2610.09540","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.09540","pdf_url":"https://arxiv.org/pdf/2610.09540","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},{"id":"doi:10.48550/arxiv.2610.09540","doi":"https://doi.org/10.48550/arxiv.2610.09540","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2610.09540","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:2610.09540","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.09540","pdf_url":"https://arxiv.org/pdf/2610.09540","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},"sustainable_development_goals":[],"study_designs":[],"awards":[],"funders":[{"id":"https://openalex.org/F4320317450","display_name":"Ho Chi Minh City University of Technology and Education","ror":"https://ror.org/05hzn5427"},{"id":"https://openalex.org/F4320326592","display_name":"Viet Nam National University Ho Chi Minh City","ror":"https://ror.org/00waaqh38"}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7220951871.pdf","grobid_xml":"https://content.openalex.org/works/W7220951871.grobid-xml"},"referenced_works_count":0,"referenced_works":[],"related_works":["https://openalex.org/W2031367896","https://openalex.org/W2587635695","https://openalex.org/W2038767521","https://openalex.org/W7027973809","https://openalex.org/W2122247361","https://openalex.org/W1964098835","https://openalex.org/W103984860","https://openalex.org/W95154907","https://openalex.org/W109057200","https://openalex.org/W2004041579"],"abstract_inverted_index":{"We":[0,76],"formulate":[1],"the":[2,20,24,28,31,37,84,92,95,105,115,126,137,158,181,190,194,198,201],"shortest-path":[3],"problem":[4,183],"in":[5],"a":[6,9,12,16,34,40,57,78,111,118,129,147,167],"domain":[7],"containing":[8],"crack":[10,29,38,116,127,138,164,171],"as":[11,56],"Hamilton--Jacobi":[13],"equation":[14],"carrying":[15],"state":[17,59],"constraint":[18],"on":[19,23,114,184],"crack,":[21],"which":[22,69],"binding":[25],"part":[26],"of":[27,33,65,83,94,99,151,160,180,200],"takes":[30],"form":[32],"variational":[35,108],"inequality:":[36],"is":[39,139],"two-sided":[41],"barrier":[42],"that":[43,53,90],"may":[44],"be":[45],"touched":[46],"and":[47,81,102,166,193],"followed":[48],"but":[49,73],"not":[50],"traversed,":[51],"so":[52],"it":[54],"acts":[55],"lower-dimensional":[58],"constraint,":[60],"carried":[61],"separately":[62],"by":[63,142],"each":[64],"its":[66],"two":[67],"lips,":[68],"admits":[70],"tangential":[71],"propagation":[72],"forbids":[74],"crossing.":[75],"establish":[77],"comparison":[79],"principle":[80],"uniqueness":[82],"value":[85],"function":[86],"through":[87],"trajectory-based":[88],"arguments":[89],"circumvent":[91],"failure":[93],"classical":[96],"doubling":[97],"technique":[98],"Crandall,":[100],"Ishii,":[101],"Lions":[103],"at":[104,162,170],"crack.":[106],"The":[107],"inequality":[109],"induces":[110],"free":[112],"boundary":[113],"separating":[117],"sliding":[119],"regime,":[120,135],"where":[121,136],"optimal":[122],"trajectories":[123],"run":[124],"along":[125],"over":[128],"finite":[130],"segment,":[131],"from":[132,175],"an":[133,185],"illuminated":[134],"reached":[140],"transversally":[141],"direct":[143],"rays;":[144],"we":[145],"give":[146],"complete":[148],"geometric":[149],"characterization":[150],"both":[152],"regimes,":[153],"including":[154],"grazing":[155],"(tangential)":[156],"contact,":[157],"absence":[159],"reflection":[161],"regular":[163],"points,":[165],"diffraction":[168],"law":[169,196],"tips,":[172],"all":[173],"derived":[174],"optimality":[176],"alone.":[177],"A":[178],"simulation":[179],"forward":[182],"exactly":[186],"solvable":[187],"configuration":[188],"reproduces":[189],"three":[191],"regimes":[192],"tip-diffraction":[195],"to":[197],"accuracy":[199],"closed-form":[202],"solution.":[203]},"counts_by_year":[],"updated_date":"2026-10-28T10:33:24.094632","created_date":"2026-10-09T00:00:00"}
