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Shi, Yongxiu; Wan, Haitao

Pointwise boundary behavior of large solutions to \(\infty\)-Laplacian equations. (English) Zbl 1492.35050

Rocky Mt. J. Math. 52, No. 3, 1047-1061 (2022).
Summary: We study the pointwise boundary behavior of the \(\infty\)-Laplacian problem \[\Delta_\infty u = b(x) f(u), \quad u \geq 0, x \in \Omega, u|_{\partial\Omega} = \infty,\] where \(b \in C(\bar{\Omega})\) is positive in \(\Omega\), \(f \in C[0, \infty) \cap C^1 (0, \infty)\) is positive and nondecreasing on \((0,\infty)\) and satisfies an Keller-Osserman type condition.

MSC:

35B40 Asymptotic behavior of solutions to PDEs
35B45 A priori estimates in context of PDEs
35D40 Viscosity solutions to PDEs
35J25 Boundary value problems for second-order elliptic equations
35J62 Quasilinear elliptic equations
35J67 Boundary values of solutions to elliptic equations and elliptic systems

Keywords:

\(\infty\)-Laplacian equation; viscosity solutions; boundary blow-up; pointwise boundary behavior
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References:

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