2 papers
math.AP2018
Laplace's equation on n-dimensional singular manifolds
Fangshu Wan
We show that the Sobolev embedding is compact on punctured manifolds with conical singularities. On the other hand, we find the Sobolev inequality does not hold on punctured manifo…
math.AP2018
Embeddings of weighted Sobolev spaces and a weighted fourth order elliptic equation
Zongming Guo, Fangshu Wan, Liping Wang
New embeddings of weighted Sobolev spaces are established. Using such embeddings, we obtain the existence and regularity of positive solutions with Navier boundary value problems f…