English

Almost minimizers for the thin obstacle problem with variable coefficients

Analysis of PDEs 2020-07-16 v1

Abstract

We study almost minimizers for the thin obstacle problem with variable H\"older continuous coefficients and zero thin obstacle and establish their C1,βC^{1,\beta} regularity on the either side of the thin space. Under an additional assumption of quasisymmetry, we establish the optimal growth of almost minimizers as well as the regularity of the regular set and a structural theorem on the singular set. The proofs are based on the generalization of Weiss- and Almgren-type monotonicity formulas for almost minimizers established earlier in the case of constant coefficients.

Keywords

Cite

@article{arxiv.2007.07349,
  title  = {Almost minimizers for the thin obstacle problem with variable coefficients},
  author = {Seongmin Jeon and Arshak Petrosyan and Mariana Smit Vega Garcia},
  journal= {arXiv preprint arXiv:2007.07349},
  year   = {2020}
}

Comments

53 pages. arXiv admin note: text overlap with arXiv:1905.11956

R2 v1 2026-06-23T17:07:27.608Z