The Dirichlet problem for the degenerate Monge-Ampère equation.

Caffarelli, Luis A., Nirenberg, Louis, and Spruck, Joel. "The Dirichlet problem for the degenerate Monge-Ampère equation.." Revista Matemática Iberoamericana 2.1-2 (1986): 19-27. <http://eudml.org/doc/39299>.

@article{Caffarelli1986,
abstract = {Let Ω be a bounded convex domain in Rn with smooth, strictly convex boundary ∂Ω, i.e. the principal curvatures of ∂Ω are all positive. We study the problem of finding a convex function u in Ω such that:det (uij) = 0 in Ωu = φ given on ∂Ω.},
author = {Caffarelli, Luis A., Nirenberg, Louis, Spruck, Joel},
journal = {Revista Matemática Iberoamericana},
keywords = {Ecuaciones diferenciales en derivadas parciales; Problema de Dirichlet; existence; smooth solution; degenerate; complex Monge-Ampère equation; plurisubharmonic function; pseudoconvex; regularity},
language = {eng},
number = {1-2},
pages = {19-27},
title = {The Dirichlet problem for the degenerate Monge-Ampère equation.},
url = {http://eudml.org/doc/39299},
volume = {2},
year = {1986},
}

TY - JOUR
AU - Caffarelli, Luis A.
AU - Nirenberg, Louis
AU - Spruck, Joel
TI - The Dirichlet problem for the degenerate Monge-Ampère equation.
JO - Revista Matemática Iberoamericana
PY - 1986
VL - 2
IS - 1-2
SP - 19
EP - 27
AB - Let Ω be a bounded convex domain in Rn with smooth, strictly convex boundary ∂Ω, i.e. the principal curvatures of ∂Ω are all positive. We study the problem of finding a convex function u in Ω such that:det (uij) = 0 in Ωu = φ given on ∂Ω.
LA - eng
KW - Ecuaciones diferenciales en derivadas parciales; Problema de Dirichlet; existence; smooth solution; degenerate; complex Monge-Ampère equation; plurisubharmonic function; pseudoconvex; regularity
UR - http://eudml.org/doc/39299
ER -