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 ϵ-regularity estimates which do not degenerate as the Lagrangians approach the critical regime given by the Willmore integrand.
| Original language | English |
|---|---|
| Article number | 10 |
| Number of pages | 39 |
| Journal | Calculus of Variations and Partial Differential Equations |
| Volume | 58 |
| Issue number | 1 |
| DOIs | |
| Publication status | Published - 1 Feb 2019 |
Cite this
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Uniform regularity results for critical and subcritical surface energies. / Bernard, Yann; Rivière, Tristan.
In: Calculus of Variations and Partial Differential Equations, Vol. 58, No. 1, 10, 01.02.2019.Research output: Contribution to journal › Article › Research › peer-review
TY - JOUR
T1 - Uniform regularity results for critical and subcritical surface energies
AU - Bernard, Yann
AU - Rivière, Tristan
PY - 2019/2/1
Y1 - 2019/2/1
N2 - 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 ϵ-regularity estimates which do not degenerate as the Lagrangians approach the critical regime given by the Willmore integrand.
AB - 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 ϵ-regularity estimates which do not degenerate as the Lagrangians approach the critical regime given by the Willmore integrand.
UR - http://www.scopus.com/inward/record.url?scp=85057856019&partnerID=8YFLogxK
U2 - 10.1007/s00526-018-1457-0
DO - 10.1007/s00526-018-1457-0
M3 - Article
VL - 58
JO - Calculus of Variations and Partial Differential Equations
JF - Calculus of Variations and Partial Differential Equations
SN - 0944-2669
IS - 1
M1 - 10
ER -