Uniform regularity results for critical and subcritical surface energies. (English) Zbl 1445.58007
Authors’ abstract: We establish regularity results for critical points to energies of immersed surfaces depending on the first and the second fundamental form exclusively. These results hold for a large class of intrinsic elliptic Lagrangians which are sub-critical or critical. They are derived using uniform \(\epsilon\)-regularity estimates which do not degenerate as the Lagrangians approach the critical regime given by the Willmore integrand.
Reviewer: Ergin Bayram (Samsun)
MSC:
| 58E15 | Variational problems concerning extremal problems in several variables; Yang-Mills functionals |
| 53A05 | Surfaces in Euclidean and related spaces |
| 35J35 | Variational methods for higher-order elliptic equations |
| 35J48 | Higher-order elliptic systems |
| 53C42 | Differential geometry of immersions (minimal, prescribed curvature, tight, etc.) |
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