Optimal regularity for rupture solutions of the infinity Laplace equation with singular absorptions (Preprint)

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Type: Preprint
National /International: International
Title: Optimal regularity for rupture solutions of the infinity Laplace equation with singular absorptions
Publication Date: 2017-12-30
Authors: - Damião J. Araújo
- José Miguel Urbano
Abstract: We consider the nonvariational singular equation, governed by the infinity Laplacian, −∆u = u−γ χ{u>0}<(sub>, γ > 1 and obtain optimal C0,αγ local regularity estimates for nonnegative viscosity solutions, where αγ=4/(3 + γ). Through a singular penalized approach, we further obtain the existence of minimal solutions, show they are nondegenerate and derive important geometric properties for the free boundary R(u) = ∂{u > 0}, the so-called rupture set.
Institution: DMUC 17-58
Online version: http://www.mat.uc.pt...prints/eng_2017.html
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