Satyanad Kichenassamy

collaborators

9 papers

math.AP2025

Symmetrization on the sphere and applications

We introduce a new method of symmetrization of mappings on the $n$ -sphere ( $n \geq 2$ ). They are applied to estimate solutions of quasilinear elliptic partial differential equations…

math.AP2025

RÃ©gularitÃ© du rayon hyperbolique

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 maximal solution of $I^ u = 4 exp (2 u)$ , which tends to $+ \infty$ as $(x,y)\t…

math.HO2025

Textual analysis of ancient Indian mathematics

Satyanad Kichenassamy

Recent analyses of Brahmagupta's discourse on the cyclic quadrilateral, and of BaudhÄyana's approximate quadrature of the circle, have shown that it is useful to submit mathematic…

math.AP2025

Renormalized variational principles and Hardy-type inequalities

Satyanad Kichenassamy

Let $I^c ◯ \subset R^{2}$ be a bounded domain on which Hardy's inequality holds. We prove that $[exp (u^{2}) - 1] / I^´^{2} \in L^{1} (I^c ◯)$ if $u \in H_{0}^{1} (I^c ◯)$ , where $I^´$ denotes the distan…

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 $I^ u = n (n - 2) u^{(n + 2) / (n - 2)}$ …