Infinity Laplacian equations with singular absorptions
Dami\~ao J. Ara\'ujo, Ginaldo de Santana S\'a
TL;DR
This paper investigates the regularity, existence, and geometric properties of solutions to singular elliptic equations governed by the infinity Laplacian, focusing on free boundary behavior.
Contribution
It provides new regularity results, existence proofs, and geometric estimates for solutions to infinity Laplacian equations with singular absorptions.
Findings
Optimal $C^{1,eta}$ regularity along the free boundary
Existence of solutions with nondegeneracy properties
Fine geometric estimates for the free boundary
Abstract
In this work, we study regularity properties for nonvariational singular elliptic equations ruled by the infinity Laplacian. We obtain optimal regularity along the free boundary. We also show existence of solutions, nondegeneracy properties and fine geometric estimates for the free boundary.
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