Embeddings of weighted Sobolev spaces and degenerate Dirichlet problems involving the weighted p-Laplacian

作者：Gol'dshtein V^*; Motreanu V V; Ukhlov A

来源：Complex Variables and Elliptic Equations, 2011, 56(10-11): 905-930.

DOI：10.1080/17476933.2011.555541

• weighted Sobolev spaces
• Dirichlet spaces
• embedding properties
• quasiconformal mappings
• Dirichlet problems
• p-Laplacian

We deal with two Dirichlet boundary value problems involving the weighted p-Laplacian. We introduce double weighted Sobolev spaces as solution spaces of the considered problems. We show the existence of weak solutions of these problems under an assumption of compact embedding involving the double weighted Sobolev spaces. Also, we establish sufficient conditions for fulfilling this embedding assumption.

• 出版日期2011