Hardy-Sobolev type inequalities in the upper half-space and their applications - Felix, Diego Dias (2019)
In this thesis, we prove two Hardy-Sobolev type inequalities and as a consequence we establish embedding results of a certain Sobolev space defined on the upper half-space into weighted Lebesgue spaces. Furthermore, some Trudinger-Moser type inequalities for functions defined in the upper half-space are obtained. As applications, we also prove existence, nonexistence and multiplicity of solutions for three class of indefinite quasilinear elliptic problems with weights in anisotropic spaces.