Yuwei Hu, Jun Zheng, Porosity of the free boundary in a minimum problem
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DOI: 10.23952/jnva.8.2024.1.06
Volume 8, Issue 1, 1 February 2024, Pages 109-124
Abstract. Given a bounded domain , a positive constant
, and functions
,
, we study geometric properties of non-negative minimizers of the minimum problem
over certain class in the framework of Orlicz-Sobolev spaces, where
denotes the positive part of
,
is the standard characteristic function, and the functions
and
satisfy the structural conditions of Lieberman-Tolksdorf’s type. In particular,
is allowed to grow with a subcritical exponent. By using the technique of blow-up and the Harnack’s inequality, we firstly prove the non-degeneracy of non-negative minimizers near the free boundary
, and then we show that the free boundary
is locally porous. Furthermore, we also prove that
has a uniformly positive density.
How to Cite this Article:
Y. Hu, J. Zheng, Porosity of the free boundary in a minimum problem, J. Nonlinear Var. Anal. 8 (2024), 109-124.