Viscosity solutions to the infinity Laplacian equation with strong absorptions
The manuscript under review considers the Dirichlet problem of the inhomogeneous \(\infty\)-Laplace equation of reaction-diffusion type. The authors first prove the existence and uniqueness of the viscosity solution via Perron's method, similar to that in [\textit{G. Lu} and \textit{P. Wang}, Adv. Math. 217, No. 4, 1838--1868 (2008; Zbl 1152.35042)]. Then they study the growth of \(u\) near the free boundary \(\{u>0\}\cap \Omega\) and obtain results similar to those in the homogeneous case [\textit{D. J. Araújo} et al., J. Funct. Anal. 270, No. 6, 2249--2267 (2016; Zbl 1344.35034)].
scientific article; zbMATH DE number 7622318
scientific article