Abstract
We consider a class of elliptic problems in the half-space R + n with nonhomogeneous boundary conditions containing nonlinearities and critical singular potentials. We obtain existence and regularity results by means of a harmonic analysis approach based on a framework of weighted spaces in Fourier variables. This framework seems to be new in the context of elliptic boundary value problems and allows us to consider Hardy's potential λ 1 / | x | 2 in R + n and Kato's potential λ 2 / | x ′ | on the boundary ∂ R + n , as well as their versions with multiple poles, without using the so-called Kato and Hardy inequalities. Singular boundary forcing terms can also be addressed. Moreover, our results cover supercritical nonlinearities, such as ± u p in R + n and ± u q on ∂ R + n with integers p > 2 ⁎ − 1 and q > 2 ⁎ − 1 .
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