Uniform estimates for elliptic equations with Caratheodory nonlinearities at the interior and on the boundary

We establish an explicit uniform a priori estimate for weak solutions to slightly subcritical elliptic problems with nonlinearities simultaneously at the interior and on the boundary. Our explicit \(L∞(Ω )\) a priori estimates are in terms of powers of their \(H^1(Ω )\) norms. To prove our result, we combine a De Giorgi-Nash-Moser iteration scheme together with elliptic regularity and the Gagliardo-Nirenberg interpolation inequality. For more information and the latex file, see https://ejde.math.txstate.edu/Volumes/2025/95/abstr.html