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Pohozaev identity for the spectral fractional Laplacian

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GST - Geometric spectral theory and applications

We present a Pohozaev identity for the Spectral Fractional Laplacian, together with its application for non-existence for some semilinear problems. The first work on non-local Pohozaev identities is the influential paper by Ros-Oton and Serra in 2014, where they consider the Restricted Fractional Laplacian. However, in our setting, the boundary behavior differs substantially and the integration by parts strategy by Ros-Oton and Serra cannot be applied. Instead, we use a spectral approach to obtain a new identity expressed as a Schur product, from which we recover the Pohozaev identity for the classical Laplacian by means of a transition matrix.

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

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