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A Caffarelli-Kohn-Nirenberg inequality in Orlicz-Sobolev spaces and applications. (English) Zbl 1251.35028

Summary: A generalization of the classical Caffarelli-Kohn-Nirenberg inequality is obtained in the setting of Orlicz-Sobolev spaces. As applications, we prove a compact embedding result, and we establish the existence of weak solutions of the Dirichlet problem for a nonhomogeneous and degenerate/singular elliptic PDE.

MSC:

35J70 Degenerate elliptic equations
35D30 Weak solutions to PDEs
35J75 Singular elliptic equations
49J45 Methods involving semicontinuity and convergence; relaxation
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