Satyanad Kichenassamy

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math.CV2025

Boundary blow-up and degenerate equations

Satyanad Kichenassamy

Let $I^c ◯ \subset R^{2}$ be a bounded domain of class $C^{2 + I^\pm}$ , $0 < I^\pm < 1$ . We show that if $u$ is the solution of $I^ u = 4 exp (2 u)$ which tends to $+ \infty$ as $(x,y)\to\partial…

math.CV2025

Boundary behavior in the Loewner-Nirenberg problem

Satyanad Kichenassamy

Let $I^c ◯ \subset R^{n}$ be a bounded domain of class $C^{2 + I^\pm}$ , $0 < I^\pm < 1$ . We show that if $n \geq 3$ and $u_{I^} c ◯$ is the maximal solution of equation $I^ u = n (n - 2) u^{(n + 2) / (n - 2)}$ …