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The solar wind is a highly turbulent plasma for which the mean rate of energytransfer $\varepsilon$ has been measured for a long time using thePolitano-Pouquet (PP98) exact law. However, this law assumes statisticalhomogeneity that can be violated by the presence of discontinuities. Here, weintroduce a new method based on the inertial dissipation $\Dis$ whoseanalytical form is derived from incompressible magnetohydrodynamics (MHD); itcan be considered as a weak and {\it local} (in space) formulation of the PP98law whose expression is recovered after integration is space. We used $\Dis$ toestimate the local energy transfer rate from the \textit{THEMIS-B} and\textit{Parker Solar Probe} (PSP) data taken in the solar wind at differentheliospheric distances. Our study reveals that discontinuities near the Sunlead to a strong energy transfer that affects a wide range of scales $\sigma$.We also observe that switchbacks seem to be characterized by a singularbehavior with an energy transfer varying as $\sigma^{-3/4}$, which slightlydiffers from classical discontinuities characterized by a $\sigma^{-1}$scaling. A comparison between the measurements of $\varepsilon$ and $\Dis$shows that in general the latter is significantly larger than the former.

Energy transfer, discontinuities and heating in the inner solar wind measured with a weak and local formulation of the Politano-Pouquet law