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On the partial regularity of energy-minimizing, area-preserving maps
| Content Provider | Semantic Scholar |
|---|---|
| Author | Evans, Lawrence Craig Gariepy, Ronald F. |
| Copyright Year | 1999 |
| Abstract | Abstract. We prove a partial regularity assertion for a Lipschitz continuous mapping u in the plane that minimizes an appropriate convex (or quasiconvex) energy functional, under the “hard” constraint that det Du = 1 a.e. The primary technical assumption is that u be nondegenerate, meaning that, locally, at least one of its partial derivatives is bounded away from zero a.e. The method of proof is to convert to a related minimization problem for a generating function w, the advantage being that we now have the “soft” constraint $w_{y_1y_2}> 0$. |
| Starting Page | 357 |
| Ending Page | 372 |
| Page Count | 16 |
| File Format | PDF HTM / HTML |
| DOI | 10.1007/s005260050145 |
| Volume Number | 9 |
| Alternate Webpage(s) | https://page-one.springer.com/pdf/preview/10.1007/s005260050145 |
| Alternate Webpage(s) | https://doi.org/10.1007/s005260050145 |
| Language | English |
| Access Restriction | Open |
| Content Type | Text |
| Resource Type | Article |
