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Almost minimizers to a transmission problem for (p,q)-Laplacian
Department of Mathematics, Uppsala University, S-751 06 Uppsala, Sweden.
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematics (Div.).ORCID iD: 0000-0002-1316-7913
2024 (English)In: Nonlinear Analysis, ISSN 0362-546X, E-ISSN 1873-5215, Vol. 241, article id 113472Article in journal (Refereed) Published
Abstract [en]

This paper concerns almost minimizers of the functional J(v,Ω)=∫Ω|Dv+|p+|Dv−|qdx,where 1<p≠q<∞ and Ω is a bounded domain of Rn, n≥1. We prove the universal Hölder regularity of local (1+ɛ)-minimizers, when ɛ is universally small. Moreover, we prove almost Lipschitz regularity of the local (1+ɛ)-minimizers, when |p−q|≪1 and ɛ≪1.

Place, publisher, year, edition, pages
Elsevier BV , 2024. Vol. 241, article id 113472
Keywords [en]
(p, q)-Laplacian, Free boundaries, Transmission problem
National Category
Mathematical Analysis
Identifiers
URN: urn:nbn:se:kth:diva-341928DOI: 10.1016/j.na.2023.113472Scopus ID: 2-s2.0-85180540661OAI: oai:DiVA.org:kth-341928DiVA, id: diva2:1824913
Note

QC 20240108

Available from: 2024-01-08 Created: 2024-01-08 Last updated: 2024-01-08Bibliographically approved

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Shahgholian, Henrik

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