Details
| Original language | English |
|---|---|
| Pages (from-to) | 25-46 |
| Number of pages | 22 |
| Journal | Calculus of Variations and Partial Differential Equations |
| Volume | 20 |
| Issue number | 1 |
| Publication status | Published - 1 May 2004 |
| Externally published | Yes |
Abstract
Given a compact Lagrangian submanifold in flat space evolving by its mean curvature, we prove uniform C2,α-bounds in space and C 2-estimates in time for the underlying Monge-Ampère equation under weak and natural assumptions on the initial Lagrangian submanifold. This implies longtime existence and convergence of the Lagrangian mean curvature flow. In the 2-dimensional case we can relax our assumptions and obtain two independent proofs for the same result.
ASJC Scopus subject areas
- Mathematics(all)
- Analysis
- Mathematics(all)
- Applied Mathematics
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In: Calculus of Variations and Partial Differential Equations, Vol. 20, No. 1, 01.05.2004, p. 25-46.
Research output: Contribution to journal › Article › Research › peer review
}
TY - JOUR
T1 - Longtime existence of the Lagrangian mean curvature flow
AU - Smoczyk, Knut
PY - 2004/5/1
Y1 - 2004/5/1
N2 - Given a compact Lagrangian submanifold in flat space evolving by its mean curvature, we prove uniform C2,α-bounds in space and C 2-estimates in time for the underlying Monge-Ampère equation under weak and natural assumptions on the initial Lagrangian submanifold. This implies longtime existence and convergence of the Lagrangian mean curvature flow. In the 2-dimensional case we can relax our assumptions and obtain two independent proofs for the same result.
AB - Given a compact Lagrangian submanifold in flat space evolving by its mean curvature, we prove uniform C2,α-bounds in space and C 2-estimates in time for the underlying Monge-Ampère equation under weak and natural assumptions on the initial Lagrangian submanifold. This implies longtime existence and convergence of the Lagrangian mean curvature flow. In the 2-dimensional case we can relax our assumptions and obtain two independent proofs for the same result.
UR - http://www.scopus.com/inward/record.url?scp=2142715277&partnerID=8YFLogxK
U2 - 10.1007/s00526-003-0226-9
DO - 10.1007/s00526-003-0226-9
M3 - Article
AN - SCOPUS:2142715277
VL - 20
SP - 25
EP - 46
JO - Calculus of Variations and Partial Differential Equations
JF - Calculus of Variations and Partial Differential Equations
SN - 0944-2669
IS - 1
ER -