Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
6425543 | Advances in Mathematics | 2016 | 29 Pages |
Abstract
Motivated by the effective bounds found in [12] for ordinary differential equations, we prove an effective version of uniform bounding for fields with several commuting derivations. More precisely, we provide an upper bound for the size of finite solution sets of partial differential polynomial equations in terms of data explicitly given in the equations and independent of parameters. Our methods also produce an upper bound for the degree of the Zariski closure of solution sets, whether they are finite or not.
Related Topics
Physical Sciences and Engineering
Mathematics
Mathematics (General)
Authors
James Freitag, Omar León Sánchez,