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Estimates on the $L^2$ norm of the positive solutions of a two parameter family of nonlinear PDE´s of the TFW type.

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GST - Geometric spectral theory and applications

In this talk I consider the two parameter family of PDE ´s (generalized TFWequation):\[\Delta u + (\gamma u – \phi) u=0,\]on $\mathbb{R}3$, where\[\phi(x)= \frac{Z}{|x|}\int_{\mathbb{R}3} \frac{u2(y)}{|x-y|} \, dy.\]Here, $Z>0$ is fixed and $\gamma \ge 0$, and $1

3}\|u\|_22 - Z$, for different values of $p$ and $\gamma$, where $u$ is thepositive solution of the generalized TFW equation. This is joint work withHeinz Siedentop (Ludwig Maximilians University).

This talk is part of the Isaac Newton Institute Seminar Series series.

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