Luigi Montoro, Berardino Sciunzi, Alessandro Trombetta
{"title":"A comparison principle for a doubly singular quasilinear anisotropic problem","authors":"Luigi Montoro, Berardino Sciunzi, Alessandro Trombetta","doi":"10.1142/s0219199723500608","DOIUrl":null,"url":null,"abstract":"<p>In this paper, we prove a comparison principle for sub-supersolutions to a singular quasilinear problem that involves the anisotropic Finsler operator <disp-formula-group><span><math altimg=\"eq-00001.gif\" display=\"block\" overflow=\"scroll\"><mrow><mo stretchy=\"false\">−</mo><msubsup><mrow><mi mathvariant=\"normal\">Δ</mi></mrow><mrow><mi>p</mi></mrow><mrow><mi>H</mi></mrow></msubsup><mi>u</mi><mo>:</mo><mo>=</mo><mo stretchy=\"false\">−</mo><mspace width=\"-.17em\"></mspace><mo>div</mo><mo stretchy=\"false\">(</mo><msup><mrow><mi>H</mi></mrow><mrow><mi>p</mi><mo stretchy=\"false\">−</mo><mn>1</mn></mrow></msup><mo stretchy=\"false\">(</mo><mo>∇</mo><mi>u</mi><mo stretchy=\"false\">)</mo><mo>∇</mo><mi>H</mi><mo stretchy=\"false\">(</mo><mo>∇</mo><mi>u</mi><mo stretchy=\"false\">)</mo><mo stretchy=\"false\">)</mo><mo>.</mo></mrow></math></span><span></span></disp-formula-group> As a main consequence, we obtain a uniqueness result for weak solutions to the problem (℘). The proof is carried out also proving a sharp regularity result of the solutions up to the boundary. Our results are new even in the euclidean case.</p>","PeriodicalId":1,"journal":{"name":"Accounts of Chemical Research","volume":null,"pages":null},"PeriodicalIF":16.4000,"publicationDate":"2024-01-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Accounts of Chemical Research","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1142/s0219199723500608","RegionNum":1,"RegionCategory":"化学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"CHEMISTRY, MULTIDISCIPLINARY","Score":null,"Total":0}
引用次数: 0
Abstract
In this paper, we prove a comparison principle for sub-supersolutions to a singular quasilinear problem that involves the anisotropic Finsler operator As a main consequence, we obtain a uniqueness result for weak solutions to the problem (℘). The proof is carried out also proving a sharp regularity result of the solutions up to the boundary. Our results are new even in the euclidean case.
期刊介绍:
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