Satyanad Kichenassamy

collaborators

Showing math.APShow all

5 papers · 1 filter

math.AP2025

Symmetrization on the sphere and applications

Satyanad Kichenassamy

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.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.AP2025

Schauder-type estimates and applications

Satyanad Kichenassamy

The Schauder estimates are among the oldest and most useful tools in the modern theory of elliptic partial differential equations (PDEs). Their influence may be felt in practically…

math.AP2025

Apodictic discourse and the Cauchy-Bunyakovsky-Schwarz inequality

Satyanad Kichenassamy

Bunyakovsky's integral inequality (1859) is one of the familiar tools of modern Analysis. We try and understand what Bunyakovsky did, why he did it, why others did not follow the s…