PreprintCC BY 4.0arXiv
Partial regularity for local minimizers of functionals with double-phase Orlicz growth
Abstract
In this paper, we consider the local minimizers to a class of non-autonomous functional with double-phase Orlicz growth: u ∈ W1,1(Ω; ℝN) ↦ ∫Ω( φ1(|Du|𝔸u) + a(x) φ2 (|Du|𝔸u) ) dx, where |Du|𝔸u := ⟨ 𝔸(x,u) Du, Du ⟩1/2 with 𝔸(x,u) = {Aαβij(x, u)}i,j = 1⋯ Nα,β= 1⋯ n as the uniformly elliptic bounded symmetric tensor field, and φk(·) for k=1,2 are two different N-functions. We prove the partial regularity of their local minimizers if the continuity modulus of a(·) and φk(·) are fit for the gap conditions, and 𝔸(x,u) meets an optimal regularity in (x,u). This is an extension from the single Orlicz growth functional to the double-phase one based on an essential improvement of several important inequalities.
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BibTeX
@misc{chang2026partial,
title = {{Partial regularity for local minimizers of functionals with double-phase Orlicz growth}},
author = {Wenrui Chang and Shenzhou Zheng},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.31242},
eprint = {2609.31242},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.31242},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Partial regularity for local minimizers of functionals with double-phase Orlicz growth
AU - Wenrui Chang
AU - Shenzhou Zheng
PY - 2026
DA - 2026/09/25
PB - arXiv
DO - 10.48550/arxiv.2609.31242
UR - https://arxiv.org/abs/2609.31242
AB - In this paper, we consider the local minimizers to a class of non-autonomous functional with double-phase Orlicz growth: u ∈ W^1,1(Ω; ℝ^N) ↦ ∫_Ω( φ_1(|Du|_𝔸^u) + a(x) φ_2 (|Du|_𝔸^u) ) dx, where |Du|_𝔸^u := ⟨ 𝔸(x,u) Du, Du ⟩^1/2 with 𝔸(x,u) = {A^αβ_ij(x, u)}_i,j = 1⋯ N^α,β= 1⋯ n as the uniformly elliptic bounded symmetric tensor field, and φ_k(·) for k=1,2 are two different N-functions. We prove the partial regularity of their local minimizers if the continuity modulus of a(·) and φ_k(·) are fit for the gap conditions, and 𝔸(x,u) meets an optimal regularity in (x,u). This is an extension from the single Orlicz growth functional to the double-phase one based on an essential improvement of several important inequalities.
ER -