An interpolation approach to $L^{\infty}$ a priori estimates for
elliptic problems with nonlinearity on the boundary
An interpolation approach to $L^{\infty}$ a priori estimates for
elliptic problems with nonlinearity on the boundary
We establish an explicit $L^\infty(\Om)$ a priori estimate for weak solutions to subcritical elliptic problems with nonlinearity on the boundary, in terms of the powers of their $H^1(\Om)$ norms. To prove our result, we combine in a novel way Moser type estimates together with elliptic regularity and Gagliardo--Nirenberg interpolation inequality. …