${l}^2$ Decoupling for certain degenerate surfaces in $\mathbb{R}^4$

Kalachand Shuin

${l}^2$ Decoupling for certain degenerate surfaces in $\mathbb{R}^4$

Classical Analysis and ODEs 2024-06-13 v2

Authors: Kalachand Shuin

Abstract

In this article, we aim to study decoupling inequality for a specific degenerate hypersurface in $\mathbb{R}^4$ . Inspired by the work of Bourgain--Demeter and Li--Zheng, we consider the hypersurface $\mathcal{S}^3_{4}:=\{(\xi_1,\xi_2,\xi_3,\xi^4_1+\xi^4_2+\xi^4_3):0\leq \xi_j\leq1, \text{for}~j=1,2,3\}$ in $\mathbb{R}^4$ and study decoupling estimates.

Keywords

hypersurfaces algebraic surfaces

Cite

@article{arxiv.2406.05056,
  title  = {${l}^2$ Decoupling for certain degenerate surfaces in $\mathbb{R}^4$},
  author = {Kalachand Shuin},
  journal= {arXiv preprint arXiv:2406.05056},
  year   = {2024}
}

Comments

15 pages. The author is thankful to Zhuoran Li for bringing into the author's knowledge that the main result of this article is closely related to the paper of C. Gao et. al. (arXiv: 2202.11326) after the submission of this article in arXiv

${l}^2$ Decoupling for certain degenerate surfaces in $\mathbb{R}^4$

Abstract

Keywords

Cite

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