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math.AP2011★ 1 cited
A Compact Embedding Theorem for Generalized Sobolev Spaces
Seng-Kee Chua, Scott Rodney, Richard L. Wheeden
We give an elementary proof of a compact embedding theorem in abstract Sobolev spaces. The result is first presented in a general context and later specialized to the case of degen…
math.AP2011
Existence of Weak Solutions of Linear Subelliptic Dirichlet Problems With Rough Coefficients
Scott Rodney
This article gives an existence theory for weak solutions of second order non-elliptic linear Dirichlet problems of the form {eqnarray} \nabla'P(x)\nabla u +{\bf HR}u+{\bf S'G}u +F…
math.AP2011★ 2 cited
Boundedness of weak solutions of degenerate quasilinear equations with rough coefficients
Dario D. Monticelli, Scott Rodney, Richard L. Wheeden
We derive local boundedness estimates for weak solutions of a large class of second order quasilinear equations. The structural assumptions imposed on an equation in the class allo…