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Regularity of vectorial minimizers for non-uniformly elliptic anisotropic integrals
Dipartimento di Matematica, UniversitΓ  di Bologna, Piazza di Porta S. Donato 5, 40126 Bologna, Italy.ORCID iD: 0000-0002-5943-5717
Univ Bologna, Dipartimento Matemat, Piazza Porta S Donato 5, I-40126 Bologna, Italy..ORCID iD: 0000-0002-9580-2879
Univ Firenze, Dipartimento Matemat & Informat U Dini, Via Morgagni 67-A, I-50134 Florence, Italy..
2025 (English)In: Nonlinear Analysis, ISSN 0362-546X, E-ISSN 1873-5215, Vol. 261, article id 113897Article in journal (Refereed) Published
Abstract [en]

We establish the local boundedness of the local minimizers 𝑒 ∢ 𝛺 β†’ Rπ‘š of non-uniformly elliptic integrals of the form βˆ«π›ΊΒ π‘“(π‘₯, 𝐷𝑣) 𝑑π‘₯, , where 𝛺 is a bounded open subset of R𝑛 (𝑛 β‰₯ 2) and the integrand satisfies anisotropic growth conditions of the type

nβˆ‘ i=1 πœ†π‘–(π‘₯)|πœ‰π‘–|𝑝𝑖 ≀ 𝑓 (π‘₯, πœ‰) ≀ πœ‡(π‘₯) {1 + |πœ‰|π‘ž}

for some exponents π‘ž β‰₯ 𝑝𝑖 > 1 and with non-negative functions πœ†π‘–, πœ‡ fulfilling suitable summability assumptions. The main novelties here are the degenerate and anisotropic behavior of the integrand and the fact that we also address the case of vectorial minimizers (π‘š > 1). Our proof is based on the celebrated Moser iteration technique and employs an embedding result for anisotropic Sobolev spaces.

Place, publisher, year, edition, pages
Elsevier, 2025. Vol. 261, article id 113897
Keywords [en]
Degenerate anisotropic growth, Local boundedness, Anisotropic Sobolev spaces, p, q-growth conditions
National Category
Mathematical Analysis
Identifiers
URN: urn:nbn:se:uu:diva-593770DOI: 10.1016/j.na.2025.113897ISI: 001531385600001Scopus ID: 2-s2.0-105009833008OAI: oai:DiVA.org:uu-593770DiVA, id: diva2:2084485
Available from: 2026-07-05 Created: 2026-07-05 Last updated: 2026-08-20Bibliographically approved

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