Hölder continuous solutions to Monge–Ampère equations

Demailly, Jean-Pierre, et al. "Hölder continuous solutions to Monge–Ampère equations." Journal of the European Mathematical Society 016.4 (2014): 619-647. <http://eudml.org/doc/277319>.

@article{Demailly2014,
abstract = {Let $(X,\omega )$ be a compact Kähler manifold. We obtain uniform Hölder regularity for solutions to the complex Monge-Ampère equation on $X$ with $L^p$ right hand side, $p>1$. The same regularity is furthermore proved on the ample locus in any big cohomology class. We also study the range $(X,\omega )$ of the complex Monge-Ampère operator acting on $\omega $-plurisubharmonic Hölder continuous functions. We show that this set is convex, by sharpening Kołodziej’s result that measures with $L^p$-density belong to $(X,\omega )$ and proving that $(X,\omega )$ has the "$L^p$-property”, $p>1$. We also describe accurately the symmetric measures it contains.},
author = {Demailly, Jean-Pierre, Dinew, Sławomir, Guedj, Vincent, Hiep, Pham Hoang, Kołodziej, Sławomir, Zeriahi, Ahmed},
journal = {Journal of the European Mathematical Society},
keywords = {Monge–Ampère operator; Kähler manifold; pluripotential theory; Hölder continuity; Monge-Ampère operator; Kähler manifold; pluripotential theory; Hölder continuity},
language = {eng},
number = {4},
pages = {619-647},
publisher = {European Mathematical Society Publishing House},
title = {Hölder continuous solutions to Monge–Ampère equations},
url = {http://eudml.org/doc/277319},
volume = {016},
year = {2014},
}

TY - JOUR
AU - Demailly, Jean-Pierre
AU - Dinew, Sławomir
AU - Guedj, Vincent
AU - Hiep, Pham Hoang
AU - Kołodziej, Sławomir
AU - Zeriahi, Ahmed
TI - Hölder continuous solutions to Monge–Ampère equations
JO - Journal of the European Mathematical Society
PY - 2014
PB - European Mathematical Society Publishing House
VL - 016
IS - 4
SP - 619
EP - 647
AB - Let $(X,\omega )$ be a compact Kähler manifold. We obtain uniform Hölder regularity for solutions to the complex Monge-Ampère equation on $X$ with $L^p$ right hand side, $p>1$. The same regularity is furthermore proved on the ample locus in any big cohomology class. We also study the range $(X,\omega )$ of the complex Monge-Ampère operator acting on $\omega $-plurisubharmonic Hölder continuous functions. We show that this set is convex, by sharpening Kołodziej’s result that measures with $L^p$-density belong to $(X,\omega )$ and proving that $(X,\omega )$ has the "$L^p$-property”, $p>1$. We also describe accurately the symmetric measures it contains.
LA - eng
KW - Monge–Ampère operator; Kähler manifold; pluripotential theory; Hölder continuity; Monge-Ampère operator; Kähler manifold; pluripotential theory; Hölder continuity
UR - http://eudml.org/doc/277319
ER -