A high-order local discontinuous Galerkin method for the <italic>p</italic>-Laplace equation
p ( o D ) e h L p ( o D ,h 1-p e ) h s(p-1) |u| p-1 W s+1,p () e h L p ( o D ,h 1-p e ) .(by Lemmas 4.9 and 4.10) Now, we provide the remaining estimates for cases p (1, 2] and p [2, +) separately.4.4.0.4.Case 1: p (1, 2].We choose = 0 in RHS( * ) in this case.Pick = + 2 = 2 in Lemma 4.15 to getandProposition 4.1, Lemma 4.17, and Proposition 2.2) hence D DG (e h ; 0) 2 L p () C 2-p g D ,f,g N n |D DG (e h ; 0)| D DG (u * h ;g D ),p,2, , e h
Authors
- Yan Xu (ORCID: https://orcid.org/0000-0001-6483-4336)
- Yue Wu (ORCID: https://orcid.org/0000-0002-8851-5513)
Institutions
- University of Science and Technology of China (CN)
- John Brown University (US)
Publication Details
- Journal
- Beijing Journal of Pure and Applied Mathematics
- Published
- 2025-01-01
- DOI
- https://doi.org/10.4310/bpam.250415002006
- Primary Topic
- Differential Equations and Numerical Methods
- Type
- article
- Field-Weighted Citation Impact
- 0.00
Funders
- National Natural Science Foundation of China