Toward Weighted Lorentz–Sobolev Capacities from Caffarelli–Silvestre Extensions
摘要
Getting inspired by the Caffarelli–Silvestre extensions, this paper investigates the weighted Lorentz–Sobolev capacities and their capacitary strong inequalities with applications to the Sobolev-type embeddings. Consequently, the weighted Lebesgue-Sobolev capacities and their applications to a functional inequality problem and the existence-regularity of solutions to the prototype p-Laplace equations with weight are addressed as well.