I am interested in the area of degenerate elliptic PDEs. This includes existence theory and regularity theory for weak solutions.

I am currently working on properties of degenerate Sobolev spaces. This includes compact embedding theorems, H=W, and weighted spaces.

Recent Work:

- with David Cruz-Uribe, SFO and Kabe Moen arXiv:1505.00699 [math.AP] - Journal reference to come soon.

- with D. D. Monticelli, and R. L. Wheeden arXiv:1411.6976 [math.AP] - Journal reference to come soon.

- with David Cruz-Uribe, SFO and Kabe Moen, Annali di Matematica Pura ed Applicata, 10.1007/s10231-015-0486-y , free version here.

- with D. D. Monticelli, arXiv:1401.4149 [math.AP] (2014) - Journal reference to come soon.

- with S-K Chua and R. L. Wheeden, Pacific Journal of Mathematics, 265, no. 1 (2013), pp. 17-59. Artilce in full available here with an older free version here.

- S. Rodney, Canadian Journal of Mathematics, 64, no. 6 (2012), pp. 1395-1414.

- with Dario Monticelli and Richard Wheeden 2011, arXiv 2011, Differential and Integral Equations 25, no.1-2 (2011), pp.143-200..

- S. Rodney, Rutgers University, Transactions of the American Mathematical Society 362 (2010), pp.673-685.