Ndvi result after sen2cor

Hi, so I performed a.cor with sen2cor at 10 meter. My AOI are mountain areas and as you can see here the slopes that are shaded receive this strange results. I am not able to use DEM at 10m as I get an error. Do you know a way to fix this, perhaps with BRDF, on this image I used the 21, option.

In my opinion for NDVI creation there is no need to make atmospheric correction. The results could be quite similar. Better correct for slope/aspect.

Well, I do need topographic correction and as far as I see the c factor is the best option but I am struggling to find a software to do it for Sentinel 2