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math.AP2026
Sharp Lifespan Dichotomies and Threshold Phenomena for Semilinear Heat Equations Driven by the Logarithmic Laplacian
Huyuan Chen, Rui Chen, Daniel Hauer +1
We study nonnegative mild solutions of \[ \partial_tu+(-Î)^{\ln}u=f(u) \qquad \text{in }(0,T)\times\mathbb R^N, \] with initial datum \(u(0,\cdot)=μu_0\), \(μ>0\). Unlike the cl…
math.AP2026
The Conformal Fractional--Logarithmic Laplacian on the Sphere: Yamabe Problems and Sharp Inequalities
Huyuan Chen, Rui Chen, Daniel Hauer
In this paper, we introduce the conformal fractional--logarithmic Laplacian on the unit sphere, defined as the derivative of the conformal fractional Laplacian with respect to the…