139 citations · 256 across the 17 of their papers we have counts for
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Symmetrization on the sphere and applications
Satyanad Kichenassamy
We introduce a new method of symmetrization of mappings on the -sphere (). They are applied to estimate solutions of quasilinear elliptic partial differential equations…
Régularité du rayon hyperbolique
Satyanad Kichenassamy
Let be a bounded domain of class , . We show that if is the maximal solution of , which tends to as $(x,y)\to\pa…
Renormalized variational principles and Hardy-type inequalities
Satyanad Kichenassamy
Let be a bounded domain on which Hardy's inequality holds. We prove that if , where denotes the distance to…
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…
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…
Breather Solutions of the Nonlinear Wave Equation
Satyanad Kichenassamy
We construct series solutions to all orders for breathers of Klein-Gordon equations, in powers of an amplitude parameter epsilon, under a sign condition on the coefficients of the…
Control of blow-up singularities for nonlinear wave equations
Satyanad Kichenassamy
While the global boundary control of nonlinear wave equations that exhibit blow-up is generally impossible, we show on a typical example, motivated by laser breakdown, that it is p…