# Almost minimizers for the thin obstacle problem with variable coefficients

@article{Jeon2020AlmostMF, title={Almost minimizers for the thin obstacle problem with variable coefficients}, author={Seongmin Jeon and Arshak Petrosyan and Mariana Smit Vega Garcia}, journal={arXiv: Analysis of PDEs}, year={2020} }

We study almost minimizers for the thin obstacle problem with variable Holder continuous coefficients and zero thin obstacle and establish their $C^{1,\beta}$ 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…

## 2 Citations

### Regularity of almost minimizers for the parabolic thin obstacle problem

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