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math.AP2019
An Improved Compact Embedding Theorem for Degenerate Sobolev Spaces
Dario D. Monticelli, Scott Rodney
This short note investigates the compact embedding of degenerate matrix weighted Sobolev spaces into weighted Lebesgue spaces. The Sobolev spaces explored are defined as the abstra…
math.AP2019
The Poisson equation on Riemannian manifolds with weighted Poincaré inequality at infinity
Giovanni Catino, Dario Daniele Monticelli, Fabio Punzo
We prove an existence result for the Poisson equation on non-compact Riemannian manifolds satisfying weighted Poincaré inequalities outside compact sets. Our result applies to a la…