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4 papers · 1 filter
A geometric characterization of a sharp Hardy inequality
Roger T. Lewis, Junfang Li, Yanyan Li
In this paper, we prove that the distance function of an open connected set in with a boundary is superharmonic in the distribution sense if and only if t…
Asymptotic Behavior of Blowup Solutions for Elliptic Equations with Exponential Nonlinearity and Singular Data
Lei Zhang
We consider a sequence of blowup solutions of a two dimensional, second order elliptic equation with exponential nonlinearity and singular data. This equation has a rich background…
A priori estimate for a family of semi-linear elliptic equations with critical nonlinearity
Lei Zhang
We consider positive solutions of on () where and are smooth functions on . If is very sub-harmonic at each critical…
Blow up and regularity for fractal Burgers equation
Alexander Kiselev, Fedor Nazarov, Roman Shterenberg
The paper is a comprehensive study of the existence, uniqueness, blow up and regularity properties of solutions of the Burgers equation with fractional dissipation. We prove existe…