Boundary Regularity for Solutions to the Linearized Monge–Ampère Equations

Boundary Regularity for Solutions to the Linearized Monge–Ampère Equations

We obtain boundary Hölder gradient estimates and regularity for solutions to the linearized Monge–Ampère equations under natural assumptions on the domain, Monge–Ampère measures and boundary data. Our results are affine invariant analogues of the boundary Hölder gradient estimates of Krylov.

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Veröffentlicht in:Archive for rational mechanics and analysis 2013-12, Vol.210 (3), p.813-836
Hauptverfasser: Le, N. Q., Savin, O.
Format: Artikel
Sprache:eng
Schlagworte:
Classical Mechanics
Complex Systems
Fluid- and Aerodynamics
Mathematical and Computational Physics
Physics
Physics and Astronomy
Theoretical
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Zusammenfassung:We obtain boundary Hölder gradient estimates and regularity for solutions to the linearized Monge–Ampère equations under natural assumptions on the domain, Monge–Ampère measures and boundary data. Our results are affine invariant analogues of the boundary Hölder gradient estimates of Krylov.
ISSN:0003-9527
1432-0673
DOI:10.1007/s00205-013-0653-5