A Comprehensive Review of Global Regularity Estimates for p(x)-Laplacian Variational Inequalities with Degenerate Matrix Weights

  • Unique Paper ID: 191571
  • Volume: 12
  • Issue: 8
  • PageNo: 7375-7377
  • Abstract:
  • This review examines the recent work by Tran, Bui, and Nguyen (2026) on global gradient regularity estimates for variational inequalities driven by p(x)-Laplacian operators with singular or degenerate matrix-valued weights. The paper establishes optimal Calderón–Zygmund type estimates and weighted Orlicz-space regularity under minimal structural assumptions, including Reifenberg-flat domains and small log-BMO matrix weights. We analyze the mathematical framework, highlight the novelty of the techniques, compare the results with existing literature, and discuss their significance and possible extensions.

Copyright & License

Copyright © 2026 Authors retain the copyright of this article. This article is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

BibTeX

@article{191571,
        author = {Megha Chandraprakash Gaikwad},
        title = {A Comprehensive Review of Global Regularity Estimates for p(x)-Laplacian Variational Inequalities with Degenerate Matrix Weights},
        journal = {International Journal of Innovative Research in Technology},
        year = {2026},
        volume = {12},
        number = {8},
        pages = {7375-7377},
        issn = {2349-6002},
        url = {https://ijirt.org/article?manuscript=191571},
        abstract = {This review examines the recent work by Tran, Bui, and Nguyen (2026) on global gradient regularity estimates for variational inequalities driven by p(x)-Laplacian operators with singular or degenerate matrix-valued weights. The paper establishes optimal Calderón–Zygmund type estimates and weighted Orlicz-space regularity under minimal structural assumptions, including Reifenberg-flat domains and small log-BMO matrix weights. We analyze the mathematical framework, highlight the novelty of the techniques, compare the results with existing literature, and discuss their significance and possible extensions.},
        keywords = {},
        month = {January},
        }

Cite This Article

Gaikwad, M. C. (2026). A Comprehensive Review of Global Regularity Estimates for p(x)-Laplacian Variational Inequalities with Degenerate Matrix Weights. International Journal of Innovative Research in Technology (IJIRT), 12(8), 7375–7377.

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