Physics Opportunities at an upgraded LHC

I will discuss the physics potential of an upgraded LHC running at an instantaneous luminosity of $10^{35}$~cm$^{-2}$s$^{-1}$.\par Based on the expected detector performances at high luminosity, the increased physics potential will be presented for a few specific physics cases, ranging from precise measurements within the Standard Model (in particular in the Higgs sector) to the discovery reach for several New Physics processes.