Abstract
Motivated by the mean field equations with probability measure derived by Sawada-Suzuki and by Neri in the context of the statistical mechanics description of two-dimensional turbulence, we study the semilinear elliptic equation with probability measure: \begin{equation*} -\Delta v=\lambda\int_IV(\alpha,x,v)e^{\alpha v}\,{\mathcal P(d\alpha)} -\frac{\lambda}{|\Omega|}\iint_{I\times\Omega}V(\alpha,x,v)e^{\alpha v}\,{\mathcal P(d\alpha)} dx, \end{equation*} defined on a compact Riemannian surface. This equation includes the above mentioned equations of physical interest as special cases. For such an equation we study the blow-up properties of solution sequences. The optimal Trudinger-Moser inequality is also considered.
Citation
Tonia Ricciardi Ricciardi. Gabriella Zecca. "Blow-up analysis for some mean field equations involving probability measures from statistical hydrodynamics." Differential Integral Equations 25 (3/4) 201 - 222, March/April 2012. https://doi.org/10.57262/die/1356012734
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