Skip to content
DraconiticResearch
Search Sources API
185,139 studies31 sourcesUpdated 54 min ago
PreprintCC BY 4.0arXiv

Regularity Estimates for Quasilinear Elliptic Equations with Measure Data and Matrix-Valued Weight

  • Sun-Sig Byun
  • Xiatong Li
  • Yeonghun Youn
Open at sourcePDFDOICite

Abstract

This paper is concerned with the existence and local gradient regularity of solutions to a quasilinear elliptic Dirichlet problem with finite Radon measure and a degenerate matrix-valued weight. Under a small log-BMO condition on 𝕄, we first prove the existence of a SOLA (solution obtained by a limit of approximations) and then establish a local Calderón-Zygmund estimate for |𝕄|1/(p−1)𝕄 Du in terms of the fractional maximal function ℳ1(μ)1/(p−1).

Related

  1. Global c1,α regularity and fine behavior at critical points for quasilinear elliptic equations with Orlicz growth and unbounded drift
    José Erivamberto Lima Oliveira
    arXivPreprintarXiv licenceFull textAnalysis & PDEsarXiv
  2. Gradient Estimates Near the Natural Exponent for Very Weak Solutions to Ap-Weighted Quasilinear Elliptic Equations
    Sun-Sig Byun, Minkyu Lim
    arXivPreprintCC BY-NC-SA 4.0Full textAnalysis & PDEsarXiv
  3. Potential estimates and improved Sobolev regularity for nonlocal fully nonlinear elliptic equations
    Yao Zhang, Lingwei Ma, Zhenqiu Zhang
    arXivPreprintarXiv licenceFull textAnalysis & PDEsarXiv
  4. Rigidity results via a Poincaré type formula for stable solutions of quasilinear anisotropic elliptic equations
    Berardino Sciunzi, Domenico Vuono
    arXivPreprintarXiv licenceFull textAnalysis & PDEsarXiv
  5. Perturbative Schauder Estimates for Q-Valued Quasilinear Elliptic Systems and a Sharp Dimension Bound for Branch Sets of Stationary Graphs
    Mattia Luchese
    arXivPreprintarXiv licenceFull textAnalysis & PDEsGeometry & topologyarXiv

Cite

BibTeXRIS
BibTeX
@misc{byun2026regularity,
  title = {{Regularity Estimates for Quasilinear Elliptic Equations with Measure Data and Matrix-Valued Weight}},
  author = {Sun-Sig Byun and Xiatong Li and Yeonghun Youn},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.09594},
  eprint = {2610.09594},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.09594},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - Regularity Estimates for Quasilinear Elliptic Equations with Measure Data and Matrix-Valued Weight
AU  - Sun-Sig Byun
AU  - Xiatong Li
AU  - Yeonghun Youn
PY  - 2026
DA  - 2026/10/07
PB  - arXiv
DO  - 10.48550/arxiv.2610.09594
UR  - https://arxiv.org/abs/2610.09594
AB  - This paper is concerned with the existence and local gradient regularity of solutions to a quasilinear elliptic Dirichlet problem with finite Radon measure and a degenerate matrix-valued weight. Under a small log-BMO condition on 𝕄, we first prove the existence of a SOLA (solution obtained by a limit of approximations) and then establish a local Calderón-Zygmund estimate for |𝕄|^1/(p−1)𝕄 Du in terms of the fractional maximal function ℳ_1(μ)^1/(p−1).
ER  -