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We present the results of an all-sky search for continuous gravitationalwaves in the public LIGO O3 data. The search covers signal frequencies $20$ Hz$\leq f \leq 800$ Hz and a spin-down range down to $-2.6\times 10^{-9}$ Hzs$^{-1}$1, motivated by detectability studies on synthetic populations ofGalactic neutron stars. This search is the most sensitive all-sky search todate in this frequency/spin-down region. The initial search was performed usingthe first half of the public LIGO O3 data (O3a), utilizing Graphical ProcessingUnits provided in equal parts by the volunteers of the Einstein@Home computingproject and by the ATLAS cluster. After a hierarchical follow-up in sevenstages, 12 candidates remain. Six are discarded at the eighth stage, by usingthe remaining O3 LIGO data (O3b). The surviving six can be ascribed tocontinuous-wave fake signals present in the LIGO data for validation purposes.We recover these fake signals with very high accuracy with our last stagesearch, which coherently combines all O3 data. Based on our results, we setupper limits on the gravitational wave amplitude $h_0$, and translate these inupper limits on the neutron star ellipticity and on the $r$-mode amplitude. Themost stringent upper limits are at $203$ Hz, with $h_0=8.1 \times 10^{-26}$ atthe 90% confidence level. Our results exclude neutron stars rotating fasterthan $5$ ms with ellipticities greater than $5\times 10^{-8}\left[{d\over{100~\textrm{pc}}}\right]$ within a distance $d$ from Earth and$r$-mode amplitudes $\alpha \geq 10^{-5}\left[{d\over{100~\textrm{pc}}}\right]$ for neutron stars spinning faster than$150$ Hz.

Deep Einstein@Home all-sky search for continuous gravitational waves in LIGO O3 public data