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.
**All pdf files linked in this section are unofficial and may contain some errors. Refer to Journals for official files/versions.
- 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 Nonlinear Analysis (2015), http://dx.doi.org/10.1016/j.na.2015.05.029
- with David Cruz-Uribe, SFO and Kabe Moen, Annali di Matematica Pura ed Applicata, 10.1007/s10231-015-0486-y
- with D. D. Monticelli, J. Differential Equations (2015), http://dx.doi.org/10.1016/j.jde.2015.05.018
- with S-K Chua and R. L. Wheeden, Pacific Journal of Mathematics, 265, no. 1 (2013), pp. 17-59.
- 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.